University of Groningen Credit supply and macroeconomic … · 2018. 3. 12. · 517798-L...

University of Groningen

Credit supply and macroeconomic fluctuationsPool, Sebastiaan

IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.

Document VersionPublisher's PDF, also known as Version of record

Publication date:2018

Link to publication in University of Groningen/UMCG research database

Citation for published version (APA):Pool, S. (2018). Credit supply and macroeconomic fluctuations. University of Groningen, SOM researchschool.

CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).

Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.

Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.

Download date: 22-08-2021

https://research.rug.nl/en/publications/credit-supply-and-macroeconomic-fluctuations(c817aafb-e92d-4cfb-8525-69b4bd07b1c5).html

517798-L-bw-Pool-SOM517798-L-bw-Pool-SOM517798-L-bw-Pool-SOM517798-L-bw-Pool-SOMProcessed on: 26-2-2018Processed on: 26-2-2018Processed on: 26-2-2018Processed on: 26-2-2018 PDF page: 1PDF page: 1PDF page: 1PDF page: 1

Credit supply and macroeconomicfluctuations

Sebastiaan Pool


Publisher: University of Groningen, Groningen, The Netherlands

Printed by: Ipskamp Printing

P.O. Box 333

7500 AH Enschede

The Netherlands

ISBN: 978-94-034-0525-4 / 978-94-034-0524-7 (ebook)

c© 2018 Sebastiaan Pool

All rights reserved. No part of this publication may be reproduced, stored in

a retrieval system of any nature, or transmitted in any form or by any means,

electronic, mechanical, now known or hereafter invented, including photo-

copying or recording, without prior written permission of the publisher.


Credit supply and macroeconomicfluctuations

PhD Thesis

to obtain the degree of PhD at the

University of Groningen

on the authority of the

Rector Magnificus, Prof. E. Sterken

and in accordance with

the decision by the College of Deans.

This thesis will be defended in public on

Thursday 22 March 2018 at 16:15 hours

by

Sebastiaan Pool

born on 26 December 1990in Deventer, The Netherlands


Supervisor

Prof. J.M. Berk

Co-supervisor

Dr. J.P.A.M. Jacobs

Assessment committee

Prof. B.J. Heijdra

Prof. C.G. de Vries

Prof. F.R. Smets


Acknowledgements

The past three years I have spent the majority of my time writing this disser-

tation. Physically I was located primarily at De Nederlandsche Bank where

I had the opportunity to glance into a tumultuous policy environment. I

remember the countless conversations with colleagues discussing contem-

porary economic issues which have not only benefited the quality of my

research, but also shaped me into a more general economist. Meanwhile I

was always able to retrieve from the fads and enjoy the tranquility of the

University of Groningen. Working for both institutions was a true pleasure

and felt like a continuation of my studies. These memories characterize the

professional, but also collegial environment I worked in. For this I am truly

thankful.

Many people in particular have contributed to this research and I would

like to express my gratitude to them. First of all, I would like to thank my

supervisor, Jan Marc Berk, for having confidence in me from the start. Your

economic insights and critical assessment on my writings have been invalu-

able for this work. Second, I would like to thank my co-supervisor Jan Jacobs

for your constructive comments on the econometric tests, but also for shar-

ing your experience in writing an academic paper. Third, I would like to

extend my thanks to my co-authors; your contribution has taken this dis-

sertation to a higher level. Niels Gilbert, thank you for sharing your policy

experience and writing skills with me. Leo de Haan, your pragmatism in

both research and policy was illuminating.

Moreover, I would like to thank a few others who have helped me to


ii Acknowledgement

write this dissertation. Jakob de Haan for offering me the opportunity to

write this dissertation and for commenting on my work repeatedly. Peter

van Els, not only for sharing your relentless enthusiasm for the economic

profession, but also for giving me constructive feedback and for taking the

heat off me occasionally. Mark Mink, for being a sounding board group

and for giving (un)solicited advice about everything, but mostly about our

shared passion: economics. Renske Maas for sharing thoughts on economics

and sports, but also for our mental reboot (coffee) twice a day.

I am truly grateful to my parents who have given me the opportunity

and provided me with the means to grow both socially and professionally.

Finally, I would like to thank Ellen Schipper for discussing anything but

economics and for unconditional support.


Contents

Acknowledgements i

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Aim of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Loan loss provisioning, bank credit and the real economy 11

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2.1 Macroeconomic framework . . . . . . . . . . . . . . . . 15

2.2.2 What does a provisioning shock do? . . . . . . . . . . . 20

2.2.3 Empirical setup . . . . . . . . . . . . . . . . . . . . . . . 21

2.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.4.1 Main results . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.4.2 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.A Model solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.B Variable names and definitions . . . . . . . . . . . . . . . . . . 35

2.C Robustness checks . . . . . . . . . . . . . . . . . . . . . . . . . 35

3 Credit defaults and bank capital 39

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39


Contents

3.2 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.2.1 The real side: households, entrepreneurs and firms . . 43

3.2.2 The financial side: banks . . . . . . . . . . . . . . . . . . 50

3.2.3 Bank recapitalizations and countercyclical buffers . . . 59

3.3 Empirical methodology . . . . . . . . . . . . . . . . . . . . . . 63

3.3.1 Calibrated parameters . . . . . . . . . . . . . . . . . . . 64

3.3.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.3.3 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.4 Empirical results . . . . . . . . . . . . . . . . . . . . . . . . . . 72

3.4.1 Technology shock . . . . . . . . . . . . . . . . . . . . . . 72

3.4.2 Credit default shock . . . . . . . . . . . . . . . . . . . . 75

3.4.3 Countercyclical capital buffer . . . . . . . . . . . . . . . 81

3.4.4 Endogenous recapitalization . . . . . . . . . . . . . . . 84

3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

3.A Model solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

3.B Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

4 Mortgage loans and shadow banks 105

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

4.2 Stylized facts extended . . . . . . . . . . . . . . . . . . . . . . . 113

4.2.1 Linear regression model . . . . . . . . . . . . . . . . . . 113

4.2.2 Multivariate regression model . . . . . . . . . . . . . . 115

4.3 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

4.3.1 Aggregate risk . . . . . . . . . . . . . . . . . . . . . . . 121

4.3.2 Real economy: households and firms . . . . . . . . . . 122

4.3.3 Regulated and shadow banks . . . . . . . . . . . . . . . 127

4.3.4 How do banks invest? . . . . . . . . . . . . . . . . . . . 130

4.3.5 Expected liquidation value . . . . . . . . . . . . . . . . 131

4.3.6 Externalities . . . . . . . . . . . . . . . . . . . . . . . . . 134

4.3.7 Closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

4.3.8 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 137

4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139


Contents

4.4.1 Growth of mortgage loans . . . . . . . . . . . . . . . . . 139

4.4.2 Shadow bank growth . . . . . . . . . . . . . . . . . . . 143

4.4.3 Liquidity risk and the lender of last resort . . . . . . . . 145

4.5 Policy options . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

4.5.1 Loan-to-value constraints . . . . . . . . . . . . . . . . . 147

4.5.2 Interest on cash . . . . . . . . . . . . . . . . . . . . . . . 149

4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

4.A Variable names and definitions . . . . . . . . . . . . . . . . . . 153

4.B Household and firm problem . . . . . . . . . . . . . . . . . . . 155

4.C Bank optimization problem . . . . . . . . . . . . . . . . . . . . 158

4.D Proof Proposition 4.1 . . . . . . . . . . . . . . . . . . . . . . . . 161

4.E Including idiosyncratic credit risk . . . . . . . . . . . . . . . . . 162

5 Sectoral allocation and macroeconomic imbalances in EMU 165

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

5.2 Stylized facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

5.3 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

5.3.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . 174

5.3.2 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

5.3.3 Monetary authority and government sector . . . . . . . 178

5.3.4 Market equilibrium conditions . . . . . . . . . . . . . . 179

5.3.5 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 180

5.4 Model simulations . . . . . . . . . . . . . . . . . . . . . . . . . 182

5.4.1 Two-region model . . . . . . . . . . . . . . . . . . . . . 182

5.4.2 Including the Rest of the World . . . . . . . . . . . . . . 186

5.4.3 Crisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

5.5 Empirical analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 187

5.5.1 Methodology and data . . . . . . . . . . . . . . . . . . . 187

5.5.2 Empirical results . . . . . . . . . . . . . . . . . . . . . . 191

5.6 Policy options and discussion . . . . . . . . . . . . . . . . . . . 193

5.6.1 Increasing competition in the nontradable sector . . . . 194

5.6.2 Deepening the internal market . . . . . . . . . . . . . . 195


Contents

5.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

5.A Sectoral dependence on domestic demand . . . . . . . . . . . . 198

5.B Model solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

5.C Including the Rest of the World . . . . . . . . . . . . . . . . . . 204

5.D Robustness checks . . . . . . . . . . . . . . . . . . . . . . . . . 206

6 Conclusion 211

6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

6.2 Policy implications . . . . . . . . . . . . . . . . . . . . . . . . . 213

6.3 Future research . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

Summary 233

Samenvatting (summary in Dutch) 237


Chapter 1

Introduction

1.1 Background

In the decades preceding the global financial crisis, the macroeconomic lit-

erature largely ignored the role of credit supply in determining macroe-

conomic fluctuations. This limited role for credit supply stands in sharp

contrast to early seminal work in the field. In the view of, e.g., Thornton

(1802), Wicksell (1898) and Fisher (1933, 1961) macroeconomic fluctuations

are, above all, caused by the expansion and contraction of credit. Similarly,

Keynes (1930, 1936) argues that credit supply, which is (in part) determ-

ined by the confidence of lenders to finance borrowers, is an important

factor in determining investment and output fluctuations. In the decades

that followed, however, the importance of fluctuations in credit supply in

the macroeconomic literature declined considerably.1 Consequently, the role

of credit supply was largely absent in the dominant class of macromodels,

the so-called Dynamic Stochastic General Equilibrium (DSGE) models, that

were developed at the turn of the millennium and widely used.2

The development of DSGE models without a central role for credit sup-

ply was supported by theory. In particular, abstracting from credit supply in

1 Economists that continued to focus on the role of credit supply in determining macroe-conomic fluctuations, most notably Minsky (1986), were no longer considered to be main-stream.

2 See e.g. Christiano et al. (2005) and Smets and Wouters (2007) for two well-known work-horse DSGE models.


2 Chapter 1

the frictionless general equilibrium framework of Arrow and Debreu (1954)

has no effect on real or nominal variables. First, Modigliani and Miller (1958)

formally showed that financial structure—the proportion of debt and equity

finance—is both indeterminate and irrelevant for real economic outcomes.

As a result, in the frictionless general equilibrium framework of Arrow and

Debreu banks could be omitted because whether representative households

finance representative firms directly or through banks is irrelevant for the

determination of real variables.

A few years later, Gurley and Shaw (1960) studied the role of financial

markets and institutions in the real economy. They argued that in a neo-

classical setting the presence of financial markets and institutions does not

restrain the ability of central banks to determine the price level. It is, how-

ever, crucial to assume demand for central-bank liabilities.3 Conditional on

demand for its liabilities, the central bank can determine and manipulate

the yield on and the quantity of its liabilities to determine and alter the price

level.4 This way, the central bank defines the unit of account and determines

all nominal variables. In the frictionless general equilibrium framework of

Arrow and Debreu no-arbitrage conditions ensure that other yields adjust

when the central bank changes the yield on or the quantity of its liabilities.

As the central bank can indirectly manipulate market yields (e.g. the Fed-

eral funds rate or the EONIA rate) to determine the price level, it is possible

in this framework to summarize banks and the central bank by a simple

interest rate rule.3 Demand for central bank liabilities ensures the existence of a general equilibrium in a

monetary economy, i.e., an equilibrium with a positive value for money, see Hahn (1984,Chapters 7 and 8) for details. Gurley and Shaw (1960) described the nature of the demandfor money, but argued that the central bank can also create demand for its liabilities by im-posing minimum reserve requirements on banks. Woodford (2000) argued that the liabilitiesof the central bank define the unit of account (euros, dollars, etc.) for all other contracts thatpeople exchange with each other. This allows central banks to determine the price level evenwithout any demand for its liabilities.

4 Specifically, Patinkin (1961) argued that the central bank can determine the price level byexogenously fixing same nominal quantity (e.g. central bank-liabilities) and some rate ofreturn (e.g. the yield on central-bank liabilities). Accordingly, the central bank can affect andmanipulate the spread between the yield on its liabilities and other market yields to bringabout desired changes in the price level, see also Woodford (2000).


Introduction 3

Apart from theoretical discussions, empirical observations in the early

days of DSGE models seemed to confirm that fluctuations in credit supply

were not a major concern for macroeconomic activity. The insights offered

by Thornton, Wicksell, Fisher and Keynes included a central role for credit

supply because, in their time, credit supply fluctuations had a noticeable

impact on macroeconomic activity. However, the period that directly pre-

cedes the recent global financial crisis was characterized by low inflation

and stable economic growth—the great moderation. In this period, it seemed

that fluctuations in credit supply had almost no impact on economic activ-

ity (Chari et al., 2007). As the role of credit supply was pushed to the back-

ground, the role of other more evident business cycle propagators such as

real and nominal rigidities, the formation of expectations and supply side

shocks dominated the macroeconomic debate.5 The lack of empirical evid-

ence corroborating the importance of fluctuations in credit supply in com-

bination with a theoretical framework in which credit supply is largely ir-

relevant, typically, trivialized the role of credit in macromodels.

The global financial crisis exemplified that deteriorating credit market

conditions are not only a reflection of a depressed real economy, but can also

be a determinant of declining economic activity. In response to the decline

in economic activity central bankers committed to unprecedented levels of

monetary accommodation. However, they could not prevent the global fin-

ancial crisis having a negative impact on the real economy that lasted for

more than a decade. The deterioration of lending conditions in credit mar-

kets was not merely a reflection of a decline in economic activity. In contrast,

the collapse of Lehman Brothers deteriorated lending conditions in credit

markets which caused a decline in credit supply. As mainstream DSGE mod-

els abstracted from credit markets altogether, they were of little use in guid-

ing policy makers on how to act. For this reason, and others, the models

were heavily criticized in the aftermath of the global financial crisis (see e.g.

Caballero (2010), Woodford (2010), Stiglitz (2011) and Romer (2016)).

5 See Mankiw (2006) for a discussion of the development of the economic debate, Lucas(1976) for a discussion of the role of expectation formation and Kydland and Prescott (1982)for the role of supply side shocks in determining macroeconomic fluctuations.


4 Chapter 1

After the outburst of the global financial crisis, the literature started to

take a closer look at the assumptions underlying the framework of Arrow-

Debreu, Modigliani-Miller and Gurley-Shaw. Progress was relatively strong,

because macroeconomists did not have to reinvent the wheel. Thornton,

Wicksell, Fisher, Keynes and their successors already provided a founda-

tion for the role of credit supply in causing macroeconomic fluctuations.

Also the literature on imperfect information with seminal contributions by

Akerlof (1970), Rothschild and Stiglitz (1976) and Townsend (1979) offered

guidance on how to relax the assumptions underlying the framework of

Arrow-Debreu, Modigliani-Miller and Gurley-Shaw. The widespread integ-

ration of frictions in the market for credit in general equilibrium macroe-

conomic models led to a so called second generation of DSGE models with

early contributions by Bernanke et al. (1999) and Kiyotaki and Moore (1997).

1.2 Aim of this thesis

This thesis aims to explore how the availability and allocation of credit af-

fects macroeconomic fluctuations. Throughout this thesis we focus on two

related issues. First, we examine the determinants of credit supply. Credit

supply is essential for economic activity. The recent global financial crisis

led to a global economic crisis when credit markets, most noticeably banks,

stopped lending to households and firms. For the same reason, the euro

area sovereign debt crisis that followed was amplified by financial markets

being unwilling or unable to lend to sovereigns. However, the build-up of

financial imbalances started with credit being structurally mis-allocated. It

is therefore important to assess whether credit is efficiently allocated, espe-

cially when its supply appears unconstrained. We therefore also examine

factors that affect the allocation of credit.


Introduction 5

1.3 Outline

In line with Gurley and Shaw (1960), much of the literature concerning mon-

etary policy is based on the assumption that the central bank directly con-

trols lending conditions in credit markets. The recent global financial crisis

demonstrated, however, that this assumption is not always appropriate. In

particular, when the banking sector is undercapitalized, monetary transmis-

sion can be impeded. To preserve monetary transmission regulators can

implement dynamic loan loss provisioning, a measure taken by the Bank

of England and Banco d’Espana.6 Dynamic provisioning for future credit

losses is forward-looking since banks estimate their expected credit losses

over the business cycle and build up provisions during upswings and draw

down on them during downturns. In contrast, backward-looking provision-

ing relates provisioning to the occurrence of problem loans which has as

potential drawback that expected credit losses are under-provisioned when

the downturn sets in.

Chapter 2 decouples the direct connection between the policy rate and

the real economy to analyze whether dynamic loan loss provisioning could

attenuate macroeconomic fluctuations. To do so, it introduces a banking sec-

tor that is exposed to credit default risk. The representative bank maxim-

izes its expected profits while it anticipates that a fraction of the credit it

supplies will not be paid back in the future. For these expected losses the

banking sector builds up provisions. In order to assess whether loan loss

provisioning affects credit supply, we estimate a panel-VAR for an unbal-

anced sample of 12 OECD countries. The results suggest that unexpected

changes in credit and loan loss provisioning are important drivers of busi-

ness cycle fluctuations. Importantly, loan loss provisioning decreases in re-

lative terms as credit supply increases which suggests that loan loss provi-

sioning is backward looking and therefore amplifies business cycle fluctu-

6 If expected losses are accurately estimated, dynamic provisioning can attenuate fluctu-ations in bank capital and credit supply. In Spain, however, credit supply was (arguably)structurally mis-allocated. Consequently, dynamic provisioning on itself was not sufficientto prevent a severe banking crisis.


6 Chapter 1

ations. In line with the Bank of England and Banco d’Espana, we therefore

advocate forward looking—dynamic—loan loss provisioning.

Whereas Chapter 2 aims to understand how credit default risk impacts

economic activity via loan loss provisioning, Chapter 3 extends this ana-

lysis by also including credit default losses. In the model an unanticipated

increase in credit default losses—a credit default shock—reduces bank cap-

ital. As credit default losses are sunk costs they should not impact the banks’

ability to issue new debt and equity to finance new credit. We fit the model

to euro area data and show, however, that credit default shocks appear to

have been a major driver of historical fluctuations in output via investment.

These results suggest that banks become constrained by their leverage ratio

after a credit default shock and reduce credit supply. Monetary transmission

is impeded because the lending rate increases even though the central bank

lowers the policy rate.

Chapter 3 studies two ex-post measures that could attenuate macroeco-

nomic fluctuations and restore monetary transmission once banks are un-

dercapitalized. Sufficient provisioning or holding large capital buffers for

expected credit default losses (as studied in Chapter 2) could, ex-ante, min-

imize the impact on economic activity as it increases the resilience of the

banking sector. Chapter 3 shows that countercyclical capital buffers as pre-

scribed by the Basel committee on Bank Supervision, i.e., lowering bank

capital regulatory requirements during a downturn and vice versa, can also

be effective in mitigating the effects of a credit default shock ex-post because

it limits the contraction in credit supply. However, there is a trade-off when

the countercyclical capital buffer is activated because banks rebuild their

capital more slowly as leverage constraints bind less. In contrast, a bank

recapitalization financed by lump-sum taxation effectively overcomes this

trade-off problem as rebuilding bank capital is no longer the bank’s choice.

To overcome moral hazard issues associated with bank recapitalizations, we

propose in Chapter 3 to follow the example set by the U.S. government and

recapitalize banks via a bail-in or an equity issuance.

Whereas Chapters 2 and 3 study how monetary transmission can be re-


Introduction 7

stored during a financial crisis to prevent a decline in credit supply, Chapters

4 and 5 focus on the build-up of imbalances that could threaten financial sta-

bility. Especially during more tranquil economic periods, imbalances could

build-up when credit is structurally mis-allocated. When these imbalances

unwind, credit default losses increase, bank capital deteriorates and credit

supply falls which might jeopardize the stability of the financial and eco-

nomic system. Chapters 4 and 5 therefore focus on factors that determine

the allocation of credit.

Chapter 4 studies how an exogenous increase in bank lending is dis-

tributed over mortgage lending versus corporate lending and how this af-

fects growth of the unregulated (shadow) banking sector versus the regu-

lated (traditional) banking sector. Both these developments may adversely

impact future economic activity. On the one hand, a reallocation of credit

supply towards mortgages to finance houses rather than corporate loans

to finance physical capital might harm the economy’s production capacity

making it eventually harder to repay mortgage debt. On the other hand,

a vastly growing shadow banking sector might increase the likelihood of

fire-sales and bank runs. Chapter 4 builds a theoretical model to show how

these two developments might be related. In particular, an exogenous in-

flow of funds in domestic banks depresses real interest rates economy-wide

and increases the share of mortgages in total bank lending. Subsequently,

the interbank market for mortgage loans becomes more liquid which in-

creases shadow banks’ competitive advantage over traditional banks and

gives rise to growth of the shadow banking sector.

Chapter 4 shows that the creation of uninsured shadow bank deposits

increases the banking sector’s reliance on liquidity insurance provided by

the central bank. The banking sector does not fully incorporate the costs of

shadow banks liquidating their assets to accommodate a run because indir-

ectly shadow banks are also insured by the liquidity provision of the central

bank. As the market (partially) ignores liquidity risk, shadow banks create

too many uninsured deposits. In Chapter 4 we argue that one way to realign

private and social interests is by offering households an interest rate on cent-


8 Chapter 1

ral bank money. If this interest rate is set correctly, the incentive for shadow

banks to finance their assets with runnable deposits rather than equity is

removed.

Chapter 5 presents a theoretical framework for a monetary union in

which an exogenous increase in credit supply is typically allocated towards

the less productive nontradable sector (which includes the housing sector).

A fall in the interest rate induces a regional demand boom and increases

demand for both tradable and nontradable goods. Whereas the nontrad-

able sector is able to increase prices and output, the tradable sector faces

foreign competition and thus has less room to increase prices. Therefore, in

real terms, capital and labor are cheaper in the nontradable sector and are

(re)allocated to this sector. As a result, the discrepancy between the external

debt level and the capacity to repay increases. This decreases the solvency

of the recipient region.

We confirm the predictions of the theoretical model by an empirical ana-

lysis that focuses on the euro area. In the decade following the introduction

of the euro, many Southern EMU members experienced a significant fall in

real interest rates and sizeable capital inflows. In a reduced-form Bayesian

panel-VAR for 10 euro area countries, the countries which experienced neg-

ative interest rate shocks (relative to the euro area average) are shown to

experience faster growth of the nontradable sector which contributed to a

deteriorating current account balance. The same reduction in interest rates,

however, did not affect growth of the tradable sector.

The allocation of credit in Chapters 4 and 5 has one important element

in common: in both chapters credit for the housing sector expands. While in

Chapter 4 the supply elasticity of the underlying asset that serves as collat-

eral determines the allocation of credit, in Chapter 5 the absence of foreign

competition for the nontradable sector allows this sector to expand. Thus,

sectors that produce goods that are both nontradable and have a low sup-

ply elasticity are therefore expected to expand and to show large price in-

creases when credit supply increases. Clearly the housing sector is the most

prevalent sector that falls in both categories.


Introduction 9

These results raise an important policy issue as to prevent excessive bor-

rowing for residential housing. A vastly growing housing sector financed

with mortgage loans could have adverse effects on future economic growth

because the economy’s production capacity does not grow in accordance

with its debt level and the housing sector is typically associated with low

productivity growth. For these reasons, some countries have introduced

constraints on admissible loan-to-value (LTV) ratios to create a precaution-

ary buffer against a decline in house prices. Chapter 4 shows that tighter

LTV constraints can indeed attenuate house price and mortgage supply fluc-

tuations. Chapter 5 suggests to liberalize the tradable sector by increasing

competition in this sector. Both interventions, tighter LTV constraints for

mortgage loans and a liberalization of the tradeable sector, reallocate funds

from the nontradeable, housing sector to more productive sectors and might

thereby benefit future economic growth and financial stability.

Finally, Chapter 6 summarizes and concludes.


Chapter 2

Loan loss provisioning, bank

credit and the real economy∗

2.1 Introduction

The recent global financial crisis has shown that bank credit is an important

determinant of business cycle fluctuations. Before the crisis, bank credit was

abundant (Adrian and Shin, 2009), boosting economic growth. During the

crisis, credit default risk, i.e., the risk that a borrower is unable to pay back

a bank loan, increased, restraining the issuance of new bank loans.

In this chapter we examine how credit default risk affects bank lending

and the business cycle. As a measure of credit default risk, we use loan loss

provisioning by banks. While most of the literature on loan loss provision-

ing examines its determinants, we are especially interested in how loan loss

provisioning affects credit and the real economy. Until now the effect of loan

loss provisioning on the real economy only received limited attention in the

literature. Furthermore, most previous studies use bank-level data instead

of macro data.

Bank loan loss provisioning may be either procyclical or countercyclical,

depending on whether provisioning is backward-looking (sometimes called

‘non-discretionary’) or forward-looking (‘discretionary’). Backward-looking

∗This chapter is based upon Pool et al. (2015).


12 Chapter 2

provisioning relates provisioning to the occurrence of problem loans. This

has as potential drawback that expected credit losses are underprovisioned

during upswings, when few problem loans are identified and hence the

level of provisioning is low. Conversely, during downturns provisioning

increases because credit defaults are high. As a result, backward-looking

provisioning is procyclical.1 In contrast, forward-looking provisioning is

countercyclical. Banks estimate their expected credit losses over the busi-

ness cycle and build up provisions during upswings and draw down on

them during downturns.

Accounting rules contribute to backward looking provisioning, as they

tend to allow provisions based on past events, not on expectations (Borio

and Lowe, 2001). International Financial Reporting Standards (IFRS) utilize

a so-called incurred loss model where loan losses are recognized only after

loss events have occurred prior to the reporting date that are likely to result

in future non-payment of loans. This is the so-called International Account-

ing Standard (IAS) 39 rule under IFRS. This rule does not allow for consid-

eration of future expected losses based on trends suggestive of additional

future losses (Bushman and Williams, 2012).

Most of the empirical finance literature confirms backward-looking pro-

visioning. Bikker and Metzemakers (2005) find evidence of a negative rela-

tion between GDP growth and provisioning for 29 OECD countries, imply-

ing backward looking practices. This procyclicality is mitigated partly by

the positive relation between banks earnings and provisions, which might

be due to either income smoothing or forward looking provisioning. Laeven

and Majnoni (2003) also find evidence that banks around the world are less

prudent during periods of rapid credit growth, in the sense that under fa-

vorable conditions banks postpone provisioning until unfavorable condi-

tions set in. Bouvatier and Lepetit (2008) examine the impact of loan loss

provisions on bank lending using a sample of 186 European banks for the

period 1992-2004. They find that backward looking provisioning amplifies

1 Bolt et al. (2012), using aggregate bank data for an unbalanced set of 17 countries over theperiod 19792007, find that loan losses are the main driver of the negative impact of recessionson bank profits.


Loan loss provisioning, bank credit and the real economy 13

credit fluctuations, while forward looking provisioning or income smooth-

ing does not. Empirical work by Jimenez et al. (2012), examining the impact

of countercyclical capital buffers on credit supply using countercyclical dy-

namic provisioning experiments in Spain, find that countercyclical capital

buffers help smooth credit supply cycles.

The usefulness of loan loss provisioning for macroprudential regulation

has recently also received attention in the theoretical literature. Bouvatier

and Lepetit (2012), in a partial equilibrium framework, show that forward-

looking provisions can eliminate procyclicality in lending standards induced

by backward-looking provisions. Agenor and Zilberman (2015), in a calib-

rated DSGE model, show that forward-looking loan loss provisions can re-

duce volatility in financial and real variables by mitigating the changes in

the stock of loan-loss reserves over the course of the business cycle. Zil-

berman and Tayler (2014) examine the interaction between loan loss provi-

sioning rules, business cycle fluctuations and monetary policy in a DSGE

model with endogenous credit risk. These authors highlight the importance

of forward-looking provisions in mitigating welfare losses, as well as how

accounting rules with respect to loan loss provisions alter the transmission

mechanism of monetary policy.

For our analysis we set up a macroeconomic framework including a

banking sector and credit default risk. The aim of the model is to under-

pin our empirical panel-VAR model with a theoretical framework. We sim-

plify an established theoretical framework to bring the model to the data.

To keep the number of variables tractable, we use an industrial organization

approach to model the banking sector (Freixas and Rochet, 1997). The rep-

resentative bank maximizes its expected profits anticipating that a fraction

of credit will default in the future (Greenbaum et al., 1989). We implicitly

solve for the optimal levels of credit and the lending rate (i.e., the price of

credit), given the short-term interest rate (the cost of credit) and credit de-

fault risk. The equilibrium conditions for credit and the lending rate are em-

bedded in a standard closed-economy macroeconomic framework, as often

used to analyze monetary transmission (see e.g., Svensson 1997 and Clarida


14 Chapter 2

et al. 1999). Hence, instead of assuming a perfect interest rate pass-through,

credit risk and market power in the banking sector determine the interest

rate spread (in line with Christiano et al. (2014) for the former and Berger

et al. (2004) for the latter). The representative bank is exposed to credit risk

which imposes a potential cost for the bank. Consequently, an increase in

credit default risk increases the lending rate and decreases bank lending.

In order to assess whether the data support our theoretical model, we

estimate a panel-VAR for an unbalanced sample of 12 OECD countries over

the last two or three decades (1980/1990-2008/9); the sample is determined

by the availability of macroeconomic provisioning data.2 Panel VARs can

be used to uncover the dynamic relationships that are common to all cross-

sectional units.3

Our panel-VAR impulse response functions (IRFs) are generally in line

with our theoretical model. First, the results suggest that credit risk (meas-

ured by provisioning by the banking sector) is one of the drivers of busi-

ness cycle fluctuations. Specifically, an increase in provisioning decreases

bank lending and economic activity. Second, it appears that banks decrease

provisioning as a percentage of total bank assets when bank lending in-

creases and vice versa. Hence, during upswings banks take on more risk by

building up relatively low provisions while in downswings, banks build up

loan loss provisions. These results confirm backward-looking provisioning.

Third, output is an important determinant of bank lending, more so than

other factors such as interest rates.

The remainder of the Chapter is structured as follows. Section 2.2 de-

scribes the theoretical model, Section 2.3 the data and Section 2.4 presents

the results. Section 2.5 concludes.2 After 2009 the OECD discontinued the publication of the Bank Profitability Statistics from

which the macroeconomic provisioning data are taken.3 For example, Love and Zicchino (2006) study the impact of financial factors on firm in-

vestment and de Haan and van den End (2013) examine banks responses to market fundingshocks. See Canova and Ciccarelli (2013) for a survey of the panel-VAR literature.



2.2 The model

This section presents the macroeconomic framework, discusses the model

predictions of a loan loss provisioning shock and describes the empirical

set-up.

2.2.1 Macroeconomic framework

Our framework is closely related to DSGE models that examine the trans-

mission of credit risk to business cycles, see e.g., Bernanke et al. (1999), Cur-

dia and Woodford (2010) and Christiano et al. (2014). As mentioned in the

Section 2.1, the aim of the model is to underpin the empirical panel-VAR

model with a theoretical framework.

The banking sector acts as an intermediary sector which lends to the real

economy at lending rate ilt and funds itself by short-term debt with a (risk-

free) short-term interest rate ist ; see Freixas and Rochet (2008). The difference

between the short-term interest rate and the lending rate consists of the term

spread and a credit risk premium. We follow the conventional approach by

assuming that the term spread is constant over time (e.g., Woodford and

Walsh 2005). Bouvatier and Lepetit (2012) show theoretically that credit risk

(accounted for via backward-looking loan loss provisioning) affects the loan

rate through at least two specific channels. If the realized number of credit

defaults is higher than anticipated, the loan rate increases because (i) expec-

ted future interest earnings decrease and (ii) the unanticipated loss deterior-

ates banks’ capital. The first effect works directly through the risk premium.

Banks update their beliefs about future defaults and increase loan loss provi-

sioning. The second effect works via the banks balance sheet. Banks increase

their loan loss provisioning to cover unanticipated losses. The decrease in

the banks capital position increases the lending rate. Here we focus on the

credit risk premium channel and leave the balance sheet channel to future

research.

Imagine a representative bank which maximizes profits from lending


16 Chapter 2

activities:

jt =(

iltϑt − is

t

)cn

t , (2.1)

where jt represents bank profits, ϑt the expected credit repayment rate, and

cnt denotes new credit and subscripts denote the time index.4 The difference

between the short-term interest rate ist (the cost price for the bank) and the

risk adjusted lending rate iltϑt is determined by the credit spread.

The credit demand curve is constructed as follows. First, we assume that

demand for new credit cnt depends negatively on the price of credit, i.e.,

the lending rate. Second, demand for new credit depends positively on the

business cycle as measured by the output gap yt. Third, demand for new

credit depends positively on the price level pt, since a high inflation rate

reduces the real interest rate ceteris paribus.5 Taking the inverse of this (by

assumption invertible) relationship with respect to the lending rate ilt, we

obtain the following relation denoted by f (·):

ilt = f

(cn

t−k, yt−k, pt−k)

, k = 0, 1, ..., q, (2.2)

where q denotes the number of lags we consider. Substituting the expres-

sion for the lending rate (2.2) into (2.1) and maximizing with respect to new

credit, yields (see Appendix 2.A):

f(cn

t−k, yt−k, pt−k)=

1ϑt

(ist − f

′ (cn


cnt

), (2.3)

where f′cn denotes the derivative of f (·) with respect to cn

t . Equation (2.3)

gives the relation between the short-term interest rate and the real economy.

It follows from (2.1) and (2.2) that the lending rate depends positively on the

short-term interest rate, ∂ilt

∂ist> 0, negatively on the expected credit repayment

4 We assume financing costs to be independent from the risk level of the banks existing bal-ance sheet. Our representative bank can always finance itself by borrowing from the centralbank at rate is

t .5 Demand for new credit may also depend on other variables not endogenously determined

in the model. We do not consider exogenous variables in our framework.



rate, ∂ilt

∂ϑt< 0, and negatively on the amount of new credit, ∂il

t∂cn

t< 0.

For ϑt, the expected credit repayment rate (2.1), we assume that banks

expect the payback rate in the next period to be equal to the payback rate

observed in the current period. This assumption of static expectations form-

ation is consistent with the empirical evidence of backward looking pro-

visioning behavior found by Laeven and Majnoni (2003) and Bikker and

Metzemakers (2005). The expected credit repayment rate is therefore:

ϑt =ct − Etdt+1

ct=

ct − dt

ct, (2.4)

where ct denotes total credit, dt denotes credit defaults, and Et· is the

expectation operator. Substituting (2.4) into (2.3) yields:

f(cn


ct

ct − dt

(ist − f

′cn(cn


cnt

). (2.5)

Since (2.5) is an implicit function for new credit, we can only implicitly solve

it for new credit and substitute the solution into the lending rate function,

(2.2). Hence, we replace cnt in (2.2) by the solution of (2.5) and find that the

lending rate is defined as a function g(·) of the following variables, see Ap-

pendix 2.A:

ilt = g(dt−k, yt−k, pt−k, is

t−k, ct−k). (2.6)

We assume that the law of motion for credit, ct, equals new credit minus

credit defaults plus the share of credit that does not mature, λ:

ct = λct−1 − dt + cnt , 0 < λ < 1, (2.7)

where the credit shock εct is incorporated in cn

t ; see Equation (2.A.7) in Ap-

pendix 2.A.6 We assume that the credit default variable, dt, follows a sta-

tionary AR(1) process that returns to its equilibrium value, a percentage δ of

6 Our representation of the banking sector is short-term oriented. We do not take into ac-count, for example, that prudential provisioning might increase credit in the long-term.


18 Chapter 2

total credit:

dt = (1− ρ)δct−1 + ρdt−1 + εpt , 0 < ρ < 1. (2.8)

Equation (2.8) states that credit defaults are a fraction of total credit in the

previous period, (1− ρ)δ, and a fraction ρ of the amount of credit defaults

in the previous period. Hence, ρ captures the persistence of credit defaults,

and (1− ρ) determines how fast the number of credit defaults returns to the

average default rate δ after a shock, denoted by εpt . The shock ε

pt is labeled a

provisioning shock, since we use bad loan provisioning data to proxy credit

default risk.

Using the solution of (2.5-2.8) we can solve the equation for total credit,

see Appendix 2.A. The model tries to estimate the effects of credit risk on

economic activity. The risk premium is linked to the degree of credit risk

and the risk-free part of the lending rate is captured by the short-term in-

terest rate. The term premium is kept constant, as mentioned above. We log-

linearize the lending rate function (2.6), the equation for total credit (2.7)

and credit defaults (2.8). Throughout this chapter, variable symbols with a

hat represent log-linearized variables, except for the interest rates ilt and is

t .

For ilt and is

t , we use that log-linearization of an interest rate under the as-

sumption that its steady state equals zero (i = 0), yields: (1+it)−(1+i)1+i = it,

which we denote by it.

The log-linearized solutions to the lending rate function, total credit and

credit defaults are embedded in a standard closed economy macroeconomic

framework, complemented by generalized versions of the aggregate de-

mand curve (2.9), the Philips curve (2.10) and the Taylor rule (2.11):

yt =Φ1(L)yt + Φ2(L)(ilt − πt) + εa

t , (2.9)

πt =Φ3(L)πt + Φ4(L)yt + εst, (2.10)

ist =γyt + ϕπt + εm

t , (2.11)

where πt denotes the inflation rate, and Φj(L) is a lag polynomial Φj(L) ≡



Φj,1L1 + ... + Φj,qLq for j = 1, 3 and Φj(L) ≡ Φj,0 + Φj,1L1 + ... + Φj,qLq for

j = 2, 4 where q denotes the number of lags we consider. The shocks, εat , εs

t

and εmt are labeled Aggregate Demand (AD) shock, Cost Push (CP) shock,

and Monetary Policy (MP) shock, respectively. The aggregate demand curve

(2.9) describes the relationship between the output gap and the real lending

rate, ilt − πt, the Philips curve (2.10) the relationship between the inflation

rate and the output gap, and the Taylor rule (2.11) the relationship between

the short-term interest rate and the inflation rate and the output gap.

Using (2.6) to substitute out the lending rate variable and imposing re-

strictions on the contemporaneousness of shocks and responses (see below),

we summarize the model as a structural Vector Auto Regressive (VAR) sys-

tem:

A(L)Zt = εt (2.12)

where we assume that εt is iid ∼ (0, Σε), Σε = Eεt, ε′t, and A(L) is a

lag polynominal of the form A(L) = A0 − A1L − ...− ApLp, in which Ak,

k = 1, ..., p, are coefficient matrices. We rewrite (2.12) into a reduced form:

Zt = B1Zt−1 + B2Zt−2 + ... + BpZ−p + vt (2.13)

where Bk ≡ A−10 Ak, vt ≡ A−1

0 εt, and vt is iid ∼ (0, Σv), Σv = Evt, v′t. We

define the vectors as follows:

Zt =[dt yt πt is

t ct

]′and εt =

[ε

pt εa

t εst εm

t εct]′

, (2.14)

where we use that: pt−pp = πt which we denote as πt.

As the reduced form disturbances, vt, represent the effect of all struc-

tural shocks in the economy, it is not possible to ascribe a particular struc-

tural shock in εt, for example a MP shock, to vt (Christiano et al., 1999).

Therefore, for identification of the structural shocks it is common practice

to assume, first, that the structural shocks are orthogonal, i.e., Σε is a diag-

onal matrix with the standard deviations on the diagonal. Second, one has


20 Chapter 2

to make identification assumptions to identify the relationship between the

reduced form VAR disturbances, vt , and the structural shocks, εt.

We use (2.13) to identify this relationship, i.e., εt = A0vt ∼ (0, Σε =

A0ΣvA′0), where A0 is the invertible square matrix in (2.12). Since A0 is a

lower triangular matrix, the structural shocks in (2.13) are identified by as-

suming a recursive system which imposes zero restrictions on all elements

of A0 above the diagonal, which is also known as a Cholesky Decomposi-

tion.

In particular, our model assumes a number of restrictions with respect

to the contemporaneous shocks and responses. The output gap, yt, is only

contemporaneously affected by provisioning and AD shocks. There is in-

deed considerable consensus in the literature that the output gap is only

modestly affected by shocks in other variables (e.g., Bernanke and Gertler

(1995) and Christiano et al. (1999)).

Inflation, πt, is assumed to be only contemporaneously affected by pro-

visioning, AD and CP shocks. The literature often assumes that prices re-

spond very sluggishly to shocks in other variables (for example, Bernanke

and Gertler (1995) and Christiano et al. (1999)).

The short-term interest rate, ist , is assumed to be contemporaneously af-

fected by provisioning, AD, CP and MP shocks.

Credit, ct, is contemporaneously affected by provisioning, AD, CP, MP

and credit shocks since new credit, cnt , contains the contemporaneous vari-

able ist . Banks assess the most recent data available to determine credit.

Credit defaults, dt, are only contemporaneously affected by provision-

ing shocks; other shocks have an impact after one period. This assumption

reflects backward-looking provisioning behavior, as empirically confirmed

by e.g., Laeven and Majnoni (2003) and Bikker and Metzemakers (2005).

2.2.2 What does a provisioning shock do?

This section discusses the predicted effects of an unanticipated change in

loan loss provisioning. The model presented in this section contains reduced

form equations and implicit functional forms. We cannot use structural para-



meters to calculate reduced form coefficients and generate theoretical im-

pulse response functions. Instead we describe the comparative statics of the

credit market after a provisioning shock in Figure 2.1.

Loan loss provisioning increases because banks expect a lower repay-

ment rate. Therefore, banks will try to compensate the expected loss by de-

creasing credit supply, see (2.6). As a consequence, credit decreases after a

positive provisioning shock, see (2.7). This is represented by a movement of

the credit supply curve in Figure 2.1 from cs0 to cs

1. The increase in the lending

rate decreases the output gap via the aggregate demand curve which causes

the inflation rate to decrease via the Philips curve. The drop in the output

gap and the inflation rate causes the credit demand curve in Figure 2.1 to

shift from cd0 to cd

1. As a consequence, the economy moves from (c0; ll0) to

(c1; ll1). Note that the total amount of credit in the economy falls unambigu-

ously, whereas the lending rate can either increase or decrease depending

on the elasticities of the credit demand and credit supply curve.

2.2.3 Empirical setup

To bring the model to the data, we estimate a reduced form panel-VAR sys-

tem adding country specific fixed effects:

Zi,t = ui + B(L)Zi,t + vi,t, (2.15)

where Zi,t is a vector of endogenous variables, i = 1, 2, ..., 12 denotes the

country index, ui is a vector of country-specific fixed effects, B(L) is a lag

polynomial B(L) ≡ B1L1 + ... + BpLp, and vi,t is a vector of stacked reduced

form residuals. The vector Zi,t consists of the endogenous variables intro-

duced in Section 2.2.1 stacked per country, Zi,t =[di,t, yi,t, πi,t, is

i,t, ci,t

]′.

The main advantage of using a panel approach is the increased efficiency

of statistical inference. High-frequency macroeconomic provisioning data

are not available and thus the number of observations is relatively small. In

VAR models the number of coefficients increases with the number of vari-

ables squared. Estimating a 5-variable VAR lacks degrees-of-freedom if time


22 Chapter 2

Figure 2.1. Static representation of an increase in provisioning.

il

c

cs0

cs1

cd0cd

1

il0

c0

il1

c1Note: the lending rate is depicted on the vertical axis and credit is depicted on the horizontalaxis. cd

τ and csτ denote the credit demand and credit supply curve at point τ = 0, 1 in time,

respectively.

series have low frequency. To overcome the degrees-of-freedom issue, we

use a panel-VAR approach. The panel-VAR approach implicitly imposes the

same underlying structure to each country in the panel. Cross-country het-

erogeneity is allowed for by adding individual fixed effects. As mentioned

in the Section 2.1, our model is macro-oriented and our focus is not on the

determinants of loan loss provisioning or income smoothing, but on the ef-

fect of loan loss provisioning on the macro-economy.7

7 For example, we assume that institutional differences between countries are time-invariant. Other, micro-oriented studies focus more on the determinants of loan loss pro-visioning. For example, Fonseca and Gonzalez (2008), using micro-data for 3221 bank-yearobservations from 40 countries, present evidence that income smoothing by managing loan



We estimate System (2.15) using the Generalized Method of Moments

(GMM). The fixed effects are eliminated by expressing all variables as de-

viation from their means. Since the fixed effects are correlated with the re-

gressors as a result of the inclusion of lags of the dependent variables, or-

dinary mean-differencing (i.e., expressing all variables as deviations from

their full sample periods means) as commonly used to eliminate fixed ef-

fects would create biased coefficients. To avoid this problem, forward mean-

differencing, also known as Helmert transformation, is used instead (cf.

Arellano and Bover 1995). This procedure removes only the forward mean,

i.e., the mean of all future observations available in the sample and pre-

serves the orthogonality between transformed variables and lagged regres-

sors, so that the lagged regressors can be used as valid instruments for es-

timating the coefficients by system GMM.8

2.3 Data

Our sample includes 12 OECD countries: Austria, Belgium, Denmark, Fin-

land, France, Germany, Italy, Japan, the Netherlands, Spain, Sweden, and

the United States. We selected developed western economies with a relat-

ively high degree of homogeneity, for which data availability, notably with

respect to loan loss provisions, was no problem. We use annual time series

of the OECD for the output gap, inflation, the short-term interest rate, out-

standing bank loans to the private sector and loan loss provisions. For de-

tails, see Table 2.B.1 in Appendix 2.B.

Expectations with respect to credit defaults is a latent variable, which

we proxy by banks’ loan loss provisioning. The provisions data series starts,

depending on the country, between 1979 and 1988 and ends either in 2008

or 2009. In order to make country comparison feasible we transform this

variable by taking the percentage of loan loss provisioning to the total bank

loss provisions depends on investor protection, disclosure, regulation and supervision, fin-ancial structure, and financial development.

8 For more details about the estimation procure we refer to Love and Zicchino (2006), whoseStata code we gratefully use for our estimation.


24 Chapter 2

Table 2.1. Summary statistics for loan loss provisions, per country.

Countries Years Mean Standard deviation Median

Austria 1989-2008 0.031 0.223 -0.024Belgium 1981-2009 -0.008 0.133 0.000Denmark 1979-2009 -0.003 0.322 -0.001Finland 1979-2009 -0.012 0.122 -0.005France 1988-2009 0.000 0.122 0.017Germany 1979-2009 0.007 0.113 -0.001Italy 1984-2009 -0.008 0.127 -0.026Japan 1989-2008 0.009 0.299 0.003Netherlands 1979-2009 -0.012 0.129 -0.009Spain 1979-2009 0.012 0.212 0.002Sweden 1979-2009 -0.028 0.912 0.033United States 1980-2009 0.057 0.252 0.009

Note: First difference of loan loss provisions as percentage of total bank assets.

balance sheet. Table 2.1 reports the descriptive statistics of loan loss provi-

sioning as percentage of total bank assets. The provisions series of France

does not start before 1988, while those of several other countries start in

1979. Provisioning is only a small percentage of the total balance sheet. Fig-

ure 2.2 shows that especially during the years before the global financial

crisis of 2008, provisioning levels were historically low for most countries

while during the global financial crisis provisioning levels started to rise

sharply.9 Table 2.2 shows the summary statistics for all transformed vari-

ables. The dimensions of the variables are: first difference of loan loss provi-

sions as percentage of total bank assets, output gap as percentage deviation

of its trend, inflation rate in percentages (first differences of logs of the price

level multiplied by 100%), short-term interest rate in levels, and credit in

9 Figure 2.2 shows that, during the late 1980s and early 1990s, loan loss provisioning inSweden, experiencing a banking crisis during the time, declines sharply. Because of this pe-culiarity, Bolt et al. (2012) drop Sweden from their sample. Results, which are not presentedhere but are available on request, show that our main findings do not change significantlywhen Sweden is omitted from the sample.



Figure 2.2. Loan loss provisions as a percentage of the total balance sheet ofthe banking sector, annual by country.

-0,5%

0,0%

0,5%

1,0%

1,5%

1979 1984 1989 1994 1999 2004 2009

(A) Austria

-0,2%

0,0%

0,2%

0,4%

0,6%

0,8%

1979 1984 1989 1994 1999 2004 2009

(B) Belgium

0,0%

0,5%

1,0%

1,5%

2,0%

1979 1984 1989 1994 1999 2004 2009

(C) Denmark

-0,2%

0,0%

0,2%

0,4%

0,6%

0,8%

1979 1984 1989 1994 1999 2004 2009

(D) Finland

-0,2%

0,0%

0,2%

0,4%

0,6%

0,8%

1979 1984 1989 1994 1999 2004 2009

(E) France

0,0%

0,2%

0,4%

0,6%

0,8%

1979 1984 1989 1994 1999 2004 2009

(F) Germany

0,0%

0,2%

0,4%

0,6%

0,8%

1979 1984 1989 1994 1999 2004 2009

(G) Italy

0,0%

0,5%

1,0%

1,5%

1979 1984 1989 1994 1999 2004 2009

(H) Japan

0,0%

0,2%

0,4%

0,6%

0,8%

1,0%

1979 1984 1989 1994 1999 2004 2009

(I) Netherlands

0,0%

0,5%

1,0%

1,5%

1979 1984 1989 1994 1999 2004 2009

(J) Spain

-4,0%

-2,0%

0,0%

2,0%

1979 1984 1989 1994 1999 2004 2009

(K) Sweden

0,0%

0,5%

1,0%

1,5%

2,0%

1979 1984 1989 1994 1999 2004 2009

(L) United States

percentage changes (first differences of the logs of total credit multiplied by

100%).

To test whether the series contain unit roots, we performed Levin et al.

(2002) panel data unit root tests after conversion into balanced panels. We

do this for the series suppressing panel-specific means, as our panel-VAR

model assumes fixed country effects so that the relevant variables to look at

are the variables after removing the panel means. The results show that all

series are stationary, see Table 2.3.10

2.4 Results

We present the main results followed by some robustness checks.

10 Alternatively, Im et al. (2003) tests for unbalanced panels confirm stationarity of all modelvariables.


26 Chapter 2

Table 2.2. Summary statistics for the model variables.

Variables Obs. Mean Standard deviation Median

dt 321 0.010 0.332 0.002yt 329 -0.104 2.411 0.029πt 527 -0.004 2.095 0.000ist 552 6.241 4.773 5.278

ct 492 8.645 6.196 8.693Note: First difference of loan loss provisions as percentage of total bank assets; output gapas percentage deviation of its trend; inflation rate in percentages (∆ logs of the price levelmultiplied by 100%); short-term interest rate in levels; credit in percentage change (∆ logs oftotal credit multiplied by 100%).

Table 2.3. Levin et al. (2002) unit-root test.

Variable Adjusted t p-Value

yt -10.97 0.00πt -6.71 0.00ct -4.84 0.00ist -5.68 0.00

dt -10.50 0.00Note:H0: Panels contain unit roots. Ha: Panels are stationary. ADF regression: 4 lags, ARparameter: common. LR variance: Bartlett kernel. Panel means not included.

2.4.1 Main results

The panel-VAR is estimated including 1 lag in line with the Akaike and

Schwarz information criteria for the individual time series. Estimation res-

ults, which for reasons of space are not presented but are available on re-

quest, prove to be robust to different lag length specifications. Instead, as

is the convention for VAR models, impulse-response functions (IRFs) are

presented.

All shocks are labeled as specified in Section 2.2. Following Jacobs and

Wallis (2005) we apply directly interpretable impulse magnitudes instead



of the conventional one standard deviation shocks, which depend on the

fit of the equations of the VAR model. The IRFs presented show the first 6

periods after the shock with 90% confidence intervals generated by Monte-

Carlo with 1000 iterations.11

This section discusses the main responses of an output gap shock (here-

after: Aggregate Demand (AD) shock) represented by a 1 percentage point

increase in the output gap, a credit shock represented by a 5 percentage

point increase in the credit growth rate, and a provisioning shock set equal

to an increase in the change in provisioning as percentage of total bank as-

sets by 0.2 percentage points. Figure 2.2 shows that many countries exper-

ienced an increase in provisioning close to 0.2 percentage point during the

beginning of the global financial crisis. In addition, Table 2.1 shows that for

many countries the standard deviation of provisioning to total bank assets

is close to 0.2. For these reasons the provisioning shock is set to a 0.2 per-

centage point increase.

The main consequences of a positive provisioning shock represented in

Figure 2.3 are a decrease of the output gap and credit (see panels B1 and

C1, respectively). The output gap declines for more than three years sug-

gesting that provisioning shocks drive business cycle fluctuations. Specific-

ally, a 0.2 percentage point increase in provisioning decreases the output

gap by approximately 0.25 percentage point suggesting a significant de-

cline in economic activity. The effect on credit becomes insignificant after

the first period. Hence, the effect of a provisioning shock on credit has no

long-lasting effects.12

Provisioning itself appears to decrease slightly three years after an AD

shock, but decreases strongly after a credit shock; see panel A2 and A3, re-

spectively. These results suggest that banks do not use economic outlook

measures to determine loan loss provisioning. The model suggests, by con-

11 We experimented with a larger number of iterations and obtained similar results.12 The IRFs of a panel-VAR excluding the provisioning variable are almost identical for thecore model variables (output gap, inflation, short-term interest rate and credit). Hence, thedestabilizing effect credit risk has on the business cycle comes from credit risk shocks, i.e.,provisioning shocks, itself, and does not affect the dynamic relations between the other vari-ables.


28 Chapter 2

Figure 2.3. Impulse response functions for provisioning, Aggregate Demand(AD) and credit shocks, annual data.

-0.2

0.0

0.2

0.4

0 3 6

(A1) Provisioning to provisioning

shock

-0.04

-0.02

0.00

0.02

0.04

0 3 6

(A2) Provisioning to AD shock

-0.3

-0.2

-0.1

0.0

0.1

0 3 6

(A3) Provisioning to credit shock

-0.6

-0.4

-0.2

0.0

0.2

0 3 6

(B1) Output gap to provisioning

Shock

0.0

0.4

0.8

1.2

0 3 6

(B2) Output gap to AD shock

0.0

1.0

2.0

3.0

0 3 6

(B3) Output gap to credit shock

-1.2

-0.8

-0.4

0.0

0.4

0 3 6

(C1) Credit to provisioning shock

-1.0

0.0

1.0

2.0

0 3 6

(C2) Credit to AD shock

0.0

2.0

4.0

6.0

0 3 6

(C3) Credit to credit shock

Note: 90% confidence intervals generated by 1000 Monte-Carlo iterations; periods in yearson the horizontal axis.

struction, that provisioning increases after a positive credit shock because

banks provision a fixed percentage of credit, δ > 0. Our finding is in line

with the empirical evidence in the literature. Cavallo and Majnoni (2002)

find for non-G10 countries a negative correlation between pre-provisioning

income and provisioning. Laeven and Majnoni (2003) present evidence that

banks delay provisioning in good times. As a consequence, provisioning

levels are too low during bad times.

The main consequence of an AD shock represented in Figure 2.3 is an

increase in credit (panel C2). The AD shock raises credit for more than 6

years. The results are in line with our theoretical framework which predicts

an increase in credit during periods of high economic activity. In addition,

the results suggest that an increase in the output gap has long-lasting ef-

fects on credit. The economic impact of the AD shock on credit is large: a 1



percentage point increase in the output gap increases credit growth by 1.5

percentage point on impact.

The main consequence of a positive credit shock, represented by a 5 per-

centage point increase in credit, is a persistent increase in the output gap up

to 1.5 percentage point (panel B3). An increase in credit supply, making more

funds available for the purchase of goods, increases aggregate demand. It

appears that credit is an important determinant of economic activity.

To determine which variables drive credit supply, we also investigate

the consequences of a CP shock (1 percentage point increase in the inflation

rate) and a MP shock (100 basis point increase in the short-term interest

rate) on credit supply. The results presented in Figure 2.4 show that credit

is unaffected by CP and MP shocks (panels C1 and C2, respectively). The

results in Figs. 2.3 and 2.4 suggest that credit is mainly affected by an AD

shock; hence, it appears that credit is primarily demand-driven.

2.4.2 Robustness

In this section we show the robustness of our findings for a different defin-

ition of the output gap and for the frequency of the observations, respect-

ively.13 Output gap measures are controversial because the output gap is

hard to estimate. To check for robustness, we replace the OECD output gap

by an output gap measure that we derived by application of the Hodrick-

Prescott (HP) filter on real annual GDP as a measure of potential output. Fig-

ure 2.C.1 in Appendix 2.C shows the same IRFs using this output gap meas-

ure which can be compared with Figure 2.3. The main results remain intact.

However, while the response of the output gap to a provisioning shock is

stronger, the response of the output gap to a credit shock becomes insigni-

ficant. Specifically, the decline in the output gap after a positive provisioning

shock is four times as large as the corresponding decline in 2.3, but lasts only

two years (compare panels B1).

13 We also tested the robustness for different selections of countries in our sample and forsub-sample periods. Results, which are not presented for reasons of space but are availableon request, show that the main conclusions remain the same.


30 Chapter 2

Figure 2.4. Impulse response functions for Cost Push (CP) and MonetaryPolicy (MP) shocks, annual data.

-0.5

0.0

0.5

1.0

1.5

0 3 6

(A1) Inflation to CP shock

-0.8

-0.4

0.0

0.4

0 3 6

(B1) Output gap to CP shock

-1.0

-0.5

0.0

0.5

1.0

0 3 6

(C1) Credit to CP shock

0.0

0.4

0.8

1.2

0 3 6

(A2) Interest to MP shock

-0.6

-0.4

-0.2

0.0

0.2

0 3 6

(B2) Output gap to MP shock

-2.0

-1.0

0.0

1.0

0 3 6

(C2) Credit to MP shock

Note: 90% confidence intervals generated by 1000 Monte-Carlo iterations; periods in yearson the horizontal axis.



The number of observations is relatively small as we use annual time

series. The reason for this is that the provisions variable—our chief vari-

able of interest—is only available at an annual frequency. Figure 2.C.2 in

Appendix 2.C shows results from a panel-VAR with four lags estimated

on quarterly data, where we interpolated the provisions series using the

quadratic match average conversion method and the HP output gap de-

rived from quarterly real GDP data.

The IRFs show that the main results remain intact. However, there are

some differences with respect to the magnitude. First, the output gap in-

creases after a positive credit shock; however, the increase is smaller than

the corresponding increase in Figure 2.3 (panel B3). Second, the decrease in

provisioning after a credit shock is smaller (panel A1). This could be due

to the fact that data interpolation does not sufficiently take into account the

volatility of provisions within the year as it smoothens the series between

two observed annual data points.

2.5 Conclusion

In this chapter we have set up a macroeconomic framework including a

banking sector and credit default risk. The banking sector maximizes profits

from lending activities anticipating that a fraction of credit will default in the

future. The solution to the banks’ optimization problem is embedded in a

macroeconomic framework. We estimated the model using a panel-VAR for

12 OECD countries over the last two or three decades to assess the import-

ance of credit default risk. Thereby we used aggregate loan loss provisioning

as a proxy for credit default risk in the banking sector.

Overall, the empirical results are in line with the predictions of the the-

oretical model. First, the results suggest that credit risk (as measured by

loan loss provisioning by banks) is one of the main drivers of business cycle

fluctuations. Specifically, an increase in provisioning decreases bank lending

and economic activity. Second, it appears that banks decrease provisioning

as a percentage of total bank assets as bank lending increases and vice versa.


32 Chapter 2

Hence, during upswings banks take on more risk by building up relatively

low provisions while in a downswing banks build up more loan loss provi-

sions. Third, output is an important determinant of bank lending, more so

than other factors such as interest rates. The sensitivity analysis shows that

our main results remain intact although the magnitude is sometimes weaker

when using a different definition for the output gap or when interpolating

annual provisions data into quarterly data for quarterly estimation.

Our macroeconomic model predictions and empirical findings confirm

the evidence found in the empirical finance literature that loan loss provi-

sions are mostly pro-cyclical and backward-looking. Whereas the literature

found that backward-looking provisioning amplifies credit fluctuations, our

macroeconomic modeling approach links provisioning behavior to the busi-

ness cycle. Our finding that loan loss provisioning has a negative impact

on bank lending and amplifies business cycle volatility, is consistent with

the findings of existing micro-oriented empirical literature, such as Bikker

and Metzemakers (2005) and Laeven and Majnoni (2003). Specifically, the in-

curred loss model, as implemented under International Accounting Stand-

ards (IAS) 39, has been viewed as recognizing impairment losses “too little

and too late” and promoting cyclicality.

One of the policy implications of our findings is that a forward-looking

loan loss provisioning practice rather than a backward-looking one is called

for to avoid pro-cyclicality. Indeed, after the global financial crisis, and sug-

gested by the Financial Stability Board, the G-20 and the Basel Committee

on Banking Supervision initiated a project to replace the incurred loss model

with the expected loss model. This has resulted into the change-over from

the incurred loss model under IAS 39 toward the expected loss model under

International Financial Reporting Standards (IFRS) 9, scheduled to become

effective in 2018 (e.g., Gaston and Song 2014). Under IFRS 9, banks will have

to provision not only for credit losses that have already occurred but also for

losses that are expected in the future. Our findings suggest that under this

new regime, the degree of pro-cyclicality induced by loan loss provisioning

will be considerably mitigated or may even disappear.



2.A Model solution

The inverse demand function is represented by the following relationship:

ilt = f

(cn


. (2.A.1)

The profit function of banks is denoted as follows:

jt =(

iltϑt − is

t

)cn

t . (2.A.2)

Substituting (2.A.1) into (2.A.2) gives:

jt =[

f(cn


ϑt − ist]

cnt . (2.A.3)

We assume that banks maximize their profits, (2.A.3), with respect to new

credit ∂jt∂cn

t= 0:

f(cn


ϑt − ist + f

′ (cn


cnt = 0,

f(cn


1ϑt

(ist − f

′ (cn


cnt

). (2.A.4)

Note, (2.A.4) is (2.3) in the main text. The credit payback probability is modeled

according the following equation:

ϑt =ct − Etdt+1

ct=

ct − dt

ct, (2.A.5)

Substituting (2.A.5) into (2.A.4) gives (2.5) in the main text:

f(cn


ct

ct − dt

(ist − f

′cn(cn


cnt

). (2.A.6)

We can solve (2.5) for new credit in period t:

cnt = −

(ct−dt

ct

)f(cn

t−k, yt−k, pt−k)− is

t

f ′cn

(cn

t−k, yt−k, pt−k) + εc

t, (2.A.7)


34 Chapter 2

where εct denotes a credit shock. Notice, however, that cn

t−k also contains the

term cnt for k = 0. Since we do implicitly assume a functional form for the

loan demand function, we cannot solve for cnt explicitly. Nevertheless, we

can postulate that, disregarding the credit shock term for the moment:

cnt = x1

(dt−k, yt−k, pt−k, is

t−k, ct−k, cnt−k−1

), (2.A.8)

where x1(·) is a function operator. We also know that:

cnt−k−1 = x2

(dt−k−1, yt−k−1, pt−k−1, is

t−k−1, ct−k−1, cnt−k−2

), (2.A.9)

where x2(·) is a function operator. Hence, we can substitute out all cnt−k and

denote cnt as a function x3(·) of the following variables:

cnt = x3


t−k, ct−k)

. (2.A.10)

Substituting (2.A.10) into (2.A.1) gives:

ilt = g


t−k, ct−k)

. (2.A.11)

For convenience we reproduce (2.7) and (2.8) from the main text, respect-

ively:

ct =λct−1 − dt + cnt , 0 < λ < 1, (2.A.12)

dt =(1− ρ)δct−1 + ρdt−1 + εpt , 0 < ρ < 1. (2.A.13)

Substituting (2.A.10) and (2.A.13) in (2.A.12) gives:

ct =λct−1 − (1− ρ)δct−1 + ρdt−1 + εpt +

x3(dt−k, yt−k, pt−k, is

t−k, ct−k)+ εc

t, (2.A.14)

We rewrite (2.A.15) as an implicit function of credit:

ct =h(dt−k, yt−k, pt−k, is

t−k, ct−k)+ εc

t, (2.A.15)



where h(·) is a function operator. We assume that the credit equation is ad-

ditively separable. Using all the contemporaneous restrictions imposed, the

model can be represented by (2.12).

2.B Variable names and definitions

See Table 2.B.1.

Table 2.B.1. Variable names and definitions.

Variable Notation Source Definition

Inflation πt OECD National Accounts ∆ log of price deflator of privateconsumption (1990 = 100) multipliedby 100%

Short-term ist IMF International Financial Three-month money market interest

interest rate Statistics (IFS) rate (%)Credit ct IMF International Financial ∆ log of bank credit to the private

Statistics (IFS) sector, deflated by the price deflatorof private consumption multipliedby 100%

Provisions dt OECD Bank Profitability First difference of net provisions, i.e.,expense set aside as allowance forbad loans, minus releases, Percentagesof total bank assets

OECD output gap yt OECD Economic Outlook Deviation of actual real GDP fromStatistics, discontinued since potential real GDP as a percentage2009 of potential real GDP

HP output gap yt Own calculations Deviation of actual real GDP frompotential real GDP as a percentageof potential real GDP. Potentialoutput calculated using the Hodrick-Prescott filter on actual output

2.C Robustness checks

See Figs. 2.C.1 and 2.C.2.


36 Chapter 2

Figure 2.C.1. Impulse response functions for provisioning, Aggregate De-mand (AD) and credit shocks

-0.1

0.0

0.1

0.2

0.3

0 3 6


shock

-2.0

-1.0

0.0

1.0

0 3 6

(B1) Output gap to provisioning shock

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0 3 6


-0.5

0.0

0.5

1.0

1.5

0 3 6


-0.01

0.00

0.01

0 3 6


-0.1

0.0

0.1

0.2

0 3 6


-0.12

-0.08

-0.04

0.00

0 3 6


-1.0

-0.5

0.0

0.5

1.0

1.5

0 3 6


0.0

2.0

4.0

6.0

0 3 6


Note: Annual data. HP output gap instead of OECD output gap. Note: 90% confidence in-tervals generated by 1000 Monte-Carlo iterations; periods in years on the horizontal axis.



Figure 2.C.2. Impulse response functions for Cost Push (CP) and MonetaryPolicy (MP) shocks, quarterly data

-0.02

-0.01

0.00

0.01

0.02

0 3 6 9 12


-0.10

-0.05

0.00

0.05

0.10

0 3 6 9 12


-0.2

-0.1

0.0

0.1

0.2

0.3

0 3 6 9 12


shock

-0.5

0.0

0.5

1.0

1.5

0 3 6 9 12


-0.4

-0.2

0.0

0.2

0.4

0 3 6 9 12


-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0 3 6 9 12


0.0

2.0

4.0

6.0

0 3 6 9 12


-0.6

-0.4

-0.2

0.0

0.2

0.4

0 3 6 9 12

(B1) Output gap to provisioning shock

-0.6

-0.4

-0.2

0.0

0.2

0 3 6 9 12


Note: 90% confidence intervals generated by 1000 Monte-Carlo iterations; periods in quar-ters on the horizontal axis.


Chapter 3

Credit defaults and bank

capital∗

3.1 Introduction

The global financial crisis demonstrated the importance of banks in determ-

ining macroeconomic fluctuations. In particular, banks started a delever-

aging process and ceased credit supply in response to the materialization of

unexpected credit defaults losses. The decline in credit supply put upward

pressure on lending rates and thereby on firms’ cost of funding. Credit de-

fault losses, however, are sunk costs and should therefore not impact the

banks’ ability to issue new debt and bank equity to finance new credit.

Even though almost a decade has passed since the start of the global finan-

cial crisis, non-performing loans are still a major problem in the euro area,

where firms are largely bank financed. The precise channels and conditions

through which credit default losses affect economic activity for a prolonged

period are, however, largely unknown.

A vast literature has studied the interactions between the financial sector,

the central bank and the real economy. Presumably the most salient line of

literature consists of, among others, Bernanke and Gertler (1989), Kiyotaki

and Moore (1997), Bernanke et al. (1999), Curdia and Woodford (2009, 2010),

∗This chapter is based upon Pool (2016).


40 Chapter 3

Del Negro et al. (2010) and Christiano et al. (2014). These models show the

importance of financial frictions caused by asymmetric information because

they increase the persistence of an adverse shock and amplify the impact

of the shock on the real economy. However, in these papers the financial

sector is often a veil because firms essentially borrow directly from house-

holds. Goodfriend and McCallum (2007), Gerali et al. (2010), Gertler and

Kiyotaki (2010) and Gertler and Karadi (2011) model the impact of bank bal-

ance sheets and leverage constraints on the real economy more explicitly. In

this chapter, we combine the literature on financial frictions and bank lever-

age constraints to account explicitly for the impact of credit default losses

on the bank balance sheet.

This chapter presents a model with an explicit role for credit default

losses on bank balance sheets to explain why credit default losses impact

economic activity. Credit default losses are introduced by augmenting a

standard Smets and Wouters (2003) model with a banking sector as in Gerali

et al. (2010) and default risk as in Bernanke and Gertler (1989) and Bernanke

et al. (1999). In addition, we allow for credit default shocks: a realization

of credit default losses different from expected credit default losses. When

credit default losses are higher than anticipated ex-ante, bank capital deteri-

orates. Banks maximize profits, but are restricted by a leverage (assets-to-

capital ratio) constraint imposed by the regulator.1 We fit the model to euro

area data. Apart from standard macroeconomic data series, we also make

use of financial data on lending rates, deposit rates, NFC-loans, household

deposits and credit spreads (Gilchrist and Mojon, 2017) to identify the credit

default shock.

The estimation results show that an unexpected increase in credit de-

fault losses raises bank leverage. This adversely impacts economic activity

because banks raise lending rates and reduce credit supply. These results

suggest that banks do not or cannot issue new bank equity and, as a con-

sequence, credit supply is constrained by their leverage ratio. The central

1 Shin (2010) shows that profit maximizing banks target leverage ratios because more riskcorresponds to potentially higher returns with limited liability for the bank equity holders.


Credit defaults and bank capital 41

bank decreases the policy rate but, as banks are constrained by their lever-

age ratio, monetary transmission is impeded and lending rates remain high.

In contrast, the deposit rate falls which reduces savings and accordingly the

economic recovery is supported by an increase in household consumption

while investment remains subdued. Inflation falls only marginally because

firms set prices as a mark-up over their marginal costs. While wages de-

cline, funding costs increase which attenuates the decline in inflation. Con-

sistent with this interpretation, the historical shock decomposition shows

that credit default shocks are a major driver of historical fluctuations in out-

put via investment.

The results in this chapter suggest that it is important for the central

bank to identify whether credit demand or credit supply is the culprit of

impeded monetary transmission. If banks are undercapitalized and are re-

luctant to issue new bank equity, lowering the policy rate resembles pushing

a string as the banks’ cost of funding is not the binding constraint and relax-

ing it has little direct impact on credit supply. While decreasing the policy

rate is advantageous as it allows banks to lower the deposit rate and sup-

ports banks to rebuild their capital, accumulating bank capital from retained

earnings is a slow process. The historical decompositions show that credit

default shocks have been an important driver of output and investment fluc-

tuations during the recent global financial crisis. Accordingly, these results

provide a structural explanation for the slow economic recovery following

the global financial crisis despite unprecedented monetary expansion.

As conventional monetary transmission is impeded, we introduce two

alternative (counterfactual) instruments that relax the binding bank capital

constraint directly: a countercyclical capital buffer and a recapitalization.

Benes and Kumhof (2015) show that countercylical capital buffers can com-

plement conventional monetary policy and lead to significant welfare in-

creases. Paries et al. (2011) also show that countercyclical capital buffers can

support monetary policy, but emphasize the importance of operating with

a lengthy implementation schedule to smooth out the transition costs for a

capital constrained banking sector. We find that countercyclical capital buf-


42 Chapter 3

fers can be effective in mitigating the effects of a credit default shock on out-

put and inflation. However, there is a trade-off because banks rebuild their

capital faster without the countercyclical capital buffer. Moreover, counter-

cyclical capital buffers only work when regulatory constraints bind while

market constraints do not. At the height of the global financial crisis, it is

doubtful whether this was the case.

In contrast, in the model a forced recapitalization overcomes this trade-

off problem as rebuilding bank capital is no longer the bank’s choice and it

also mitigates market constraints. A recapitalization can therefore be an ef-

fective instrument to attenuate output and inflation fluctuations when banks

are undercapitalized. Although the degree of effectiveness depends on how

the recapitalization is financed, the results are in general straightforward. As

the household in this model is both the taxpayer, the bank equity holder and

the depositor, converting deposits into bank equity or a government facilit-

ated bank loan has only little negative impact. The claim of households on

the cash flows generated by the bank is after all unaffected. Meanwhile, the

bank leverage constraint relaxes and therefore the recapitalization restores

monetary transmission and enables a faster economic recovery.

The discussion in this chapter focuses on the potential costs of a bank

recapitalization in the short-run. As bank failure is ruled out a priori and

issues like moral hazard that rise in accordance with a recapitalization are

ignored, the long-run consequences of a bank recapitalization are not clear-

cut. Nevertheless, our results do suggest that measures that relax the bank

capital constraint when banks are undercapitalized support the economic

recovery. These results support empirical and theoretical evidence presen-

ted by Berger and Bouwman (2013) and Clerc et al. (2015), respectively, who

show that an increase in bank capital enhances bank performance during a

banking crisis.

The remainder of this chapter is structured as follows. Section 3.2 de-

scribes the model. Section 3.3 discusses the data, the calibration and the

Bayesian methodology. Section 3.4 presents the estimation results. Section

3.5 concludes.



3.2 The model

The model contains two types of agents, households denoted by the super-

script H and entrepreneurs denoted by E who operate the firms. The real

side of the model comes from Smets and Wouters (2003). Households and

entrepreneurs interact via a banking sector which competes in a monopol-

istic competitive environment because they offer heterogeneous financial

products, see Gerali et al. (2010). Entrepreneurs borrow to invest in cap-

ital and operate the intermediate firms to produce an intermediate product.

Intermediate firms might default on their loan. Default risk is introduced

by augmenting the model with a Bernanke et al. (1999) financial accelerator

mechanism.

3.2.1 The real side: households, entrepreneurs and firms

Households

The representative household maximizes its expected utility by choosing

consumption, leisure and deposits.2 The inter-temporal utility function is

separable in consumption and leisure:

maxCH

t (i),1−LHt (i),Dt(i)

Et

∞

∑t=0

(βH)tU(CHt (i), LH

t (i)), (3.1)

where

U(CHt (i), LH

t (i)) ≡ ηct

([CH

t (i)− hCHt−1(i)

]1−σc

1− σc−

ηlt[LH

t (i)]1+σh

1 + σh

),

(3.2)

where CHt (i) denotes consumption of agent i at time t, LH

t (i) denotes hours

worked, Dt(i) denotes deposits, βH is the household discount factor, Et is

an expectation operator, σc is the coefficient of relative risk aversion (inverse

2 Here we consider a cashless limit economy, similar to e.g. Smets and Wouters (2007) andGerali et al. (2010). Consequently, the role of liquidity cannot be analyzed as in e.g. Christianoet al. (2005), Goodfriend and McCallum (2007) and Mierau and Mink (2016).


44 Chapter 3

of the inter-temporal elasticity of substitution), σh represents the inverse of

the elasticity of work effort with respect to the real wage, h denotes the

habit parameter, ηct and ηl

t represent a preference shock and a labor sup-

ply shock, respectively. Both shocks follow a stochastic process of the form

ηct = ρcηc

t−1 + εct and ηl

t = ρlηlt−1 + εl

t, 0 < ρb, ρl < 1, where εct and εl

t are

i.i.d. error terms ∼ (µc, σc) and i.i.d.∼ (µl , σl).3 The representative house-

hold maximizes expected utility subject to a series of budget constraints:

CHt (i) + Dt(i) = wtLH

t (i) +1 + rd

t−1

πtDt−1(i) + Πt(i) + (1−ωb)Jt(i)− Tt,

(3.3)

where wt denotes the real household wage Wt/Pt, where Pt denotes the

price level, πt ≡ Pt/Pt−1 is the inflation rate, rdt is the deposit rate such that

(1 + rdt−1)Dt−1(i)/πt denotes real interest income on last period’s deposits,

Πt(i) and (1− ωb)Jt(i) denote real profits from the intermediate firms and

real profits from the banking sector that households’ receive in a lump-sum

fashion (so households are the true owners of the firms and the banks) and

Tt is a lump-sum tax levied by the central bank for the recapitalization of the

banking sector.4

Households are wage setters in the labor market. We adopt a commonly

used wage-adjustment formulation which is a variant of Calvo (1983) pri-

cing. Following Smets and Wouters (2003), we assume that wages can only

change after receiving a random wage signal. The probability of receiving

the signal is equal to 1− ξw. If a household receives a wage signal, it sets a

new wage denoted by Wt. In addition, if no wage signal is received, wages

are indexed partially. If households cannot re-optimize, the wage rate is in-

3 All stochastic shocks are specified as a linear process as the model is eventually linearizedaround its steady state. The non-linear process could be represented by ηt = ρηt−1 + (1−ρ) + εt such that in steady state η∗ = 1.

4 We follow the mainstream approach and assume that actuarially fair priced state-contingent securities exist that insure each household against idiosyncratic variations inlabor and dividend income. Consequently, as in the Arrow-Debreu model individual house-hold income will correspond to aggregate household income.



dexed according the following indexation equation:

Wt(i) =(

Pt−1

Pt−2

)γw

Wt−1(i), (3.4)

where γw is the degree of wage indexation. Households maximize utility

(3.1) subject to the budget constraint (3.3) and demand for labor which is

assumed to be represented by:

LHt (i) =

(Wt(i)

Wt

)−(1+λwt )/(λ

wt )

LHt , (3.5)

where λwt = λw + ηw

t determines the wage mark-up, ηwt is a wage cost-push

shock following a stochastic progress: ηwt = ρwηw

t−1 + εwt , 0 < ρw < 1, where

εwt is an i.i.d. error term ∼ (µw, σw). The maximization problems results in

a wage mark-up equation which determines with Equation (3.4) the law of

motion for the wage process, i.e., the so-called New Keynesian wage curve,

see Appendix 3.A.

Entrepreneurs

Entrepreneurs operate the intermediate firms. They invest in real physical

capital Kt at time t which has a nominal price qt and use capital together with

labor to produce. The capital accumulation identity is denoted as follows:

Kt(j) ≡ (1− δk)Kt−1(j) +[

1− ψ

(ηi

t It(j)It−1(j)

)]It(j), (3.6)

where It(j) denotes investment by entrepreneur j, and ψ(·) captures capital

adjustment costs, where ψ(·)′ > 0, ψ(·)′′ < 0. Following Christiano et al.

(2005), we assume that ψ(·) = 0 and ψ′(·) = 0 in steady state, so the ad-

justment costs will only depend on the second-order derivative ψ′′(·). Here

ηit is an investment shock which follows a stochastic process of the form

ηit = ρiηi

t−1 + εit where εi

t is an i.i.d. error term ∼ (µi, σi).

Return to capital is subject to idiosyncratic risk. Ex-post gross return to

capital is given by ωt(j)rkt where ωt(j) is an idiosyncratic disturbance term


46 Chapter 3

realized by entrepreneur j and rkt is the aggregate gross return on capital av-

eraged over all firms. Similar to Bernanke et al. (1999), we assume that ωt(j)

is independently and identically distributed across entrepreneurs and time

and follows a log-normal distribution with density and cumulative distri-

butions functions denoted by f (ωt(j)) and F(ωt(j)), respectively.

The entrepreneur finances the acquisition of capital with its income in

the previous period and borrows the remaining funds from the banking

sector pledging expected return to capital (Etωt+1(j) rkt+1qtKt(i)) as col-

lateral. Households will not directly finance entrepreneurs because, by as-

sumption, they do not have the means or skills to eliminate all idiosyn-

cratic risk via diversification. If the realization of ωt(j) is below a certain

threshold ωt, the firm defaults because realized return to capital is insuf-

ficient to repay the amount borrowed. The entrepreneur chooses physical

capital, the amount of borrowing and a default threshold by maximizing

the firm’s expected return to capital given a gross non-default lending rate

rbt . The threshold below which the entrepreneur defaults is set according:

rbt Bt(j) = Etωt+1rk

t+1qtKt(i), (3.7)

where Bt(j) denotes the amount borrowed by the entrepreneur. Hence, the

expected default threshold, Etωt+1 = (rbt Bt(j))/(Etrk

t+1qtKt(j)) is de-

termined by the relation between the gross non-default lending rate and the

expected aggregate gross return to capital averaged over all firms rbt /rk

t+1

and a measure related to entrepreneurial leverage, Bt(j)/(qtKt(j)).

Figure 3.1 graphically describes the payoff structure of the loan contract.

If realized return ωt(j) > ωt, the entrepreneur repays the debt rbt Bt(j) and

is entitled to any remaining profits (the area below to dotted 45 degree line

and to the right of ωtrkt qt−1Kt−1 on the x-axis minus the debt repayment

rbt Bt(j)). If ωt(j) < ωt, realized return is insufficient to repay the loan and

the entrepreneur defaults without realizing any profits. The entrepreneur’s

stake in the project is therefore similar to common bank equity. If the entre-

preneur defaults the banks can only recover a fraction (1− µ) of the gross



return, where 0 < µ < 1 denotes the cost of default. In case of default the

banks claim the project’s total return after paying default costs and receive

(1− µ)ωt(j)rkt qt−1Kt−1(j) and lose the remaining part, see Figure 3.1. Thus,

the entrepreneur uses the project’s expected return to capital as collateral.

Figure 3.1. Payoff structure of the loan contract.

Bank return

Total return45

µωtrkt qt−1Kt−1

rbt Bt

ωtrkt qt−1Kt−1

All entrepreneurs who realize an idiosyncratic disturbance term ωt(i) <

ωt default. Using the cumulative distribution function and the law of large

numbers, the fraction of loans that default at period t can be expressed as

F(ωt) =∫ ωt

0 f (ωt)dωt. Using the same notation as in Bernanke et al. (1999)

Γ(ωt) is the share of gross return to capital that goes to the bank:

Γ(ωt) ≡∫ ωt

0ωt f (ωt)dωt + ωt

∫ ∞

ωt

f (ωt)dωt, (3.8)

and µG(ωt) is the share of gross returns that is lost in the bankruptcy pro-


48 Chapter 3

cess:

µG(ωt) ≡ µ∫ ωt

0ωt f (ωt)dωt. (3.9)

Hence, the net share of gross profits that the bank appropriates is equal to

Γ(ωt)− µG(ωt). The financial intermediary has opportunity costs denoted

by the riskless gross rate of return rt, which is the interest rate set by the cent-

ral bank. However, different from the financial intermediaries in Bernanke

et al. (1999), the banking sector might be balance sheet constrained. When

the bank is balance sheet constrained, its appropriate opportunity costs are

no longer the risk-free rate, but a higher lending interest rate, rwbt . The bank

will therefore only agree with the loan contract if it receives on average at

least this lending rate.

Entrepreneurs’ optimization problem

Entrepreneurs only care for consumption. They maximize the discounted

sum of expected future utility, where the utility function takes a logarithmic

form, by choosing consumption, capital, loans, the default threshold value,

the capital utilization rate, and labor input (CEt (j), Kt(j), Bt(j), ωt+1(j), ut(j)

and LHt (j)):

maxCE

t ,Kt,Bt,ωt+1,ut,LHt

Et

∞

∑t=0

(βE)t ln

CEt − hCE

t−1

subject to their budget constraint:

Bt(j) =1 + rb

t−1 [1− Γ(ωt(j))]πt

Bt−1(j)−

Et

[1− Γ(ωt+1(j))]

[rk

t+1ut − ψ(ut)]

Kt(j)+

It(j) + wtLHt (j) + CE

t (j), (3.10)



the capital accumulation identity (3.6) and the participation constraint of the

banks:

Et

[Γ(ωt+1(j))− µG(ωt+1(j))

]rk

t+1utqtKt(j)≥ rwb

tEt πt+1

Bt(j),

(3.11)

where ψ(ut(j))Kt−1(j) is the real cost of setting a capital utilization rate

equal to ut and δk is the depreciation rate of physical capital. Inequality

(3.11) states that banks invest only if they expect the project’s return to be

higher than their opportunity costs of supplying credit denoted by rwbt . In

the steady state this opportunity cost is equal to the risk-free interest rate rt.

Banks, however, might be constrained by the amount of capital they have. In

that case, capital requirements limit the bank to supply more credit which

raises the lending rate. As the right hand side of (3.11) increases the left

hand side must increase as well. That is, if credit conditions tighten firms

need more capital, a higher rate of return, higher capital prices or a lower

default probability to obtain a similar amount of funding.

Intermediary firms and retailers

Intermediate firm j produces a unique variety of a wholesale good Yt(j)

according to the following Cobb-Douglas production function:

Yt(j) = ηat AtKt(j)αLH

t (j)1−α, (3.12)

where At is a Hicks-neutral technology parameter and ηat is a technology

shock which follows a stochastic progress of the form ηat = ρaηa

t−1 + εat where

εat is an i.i.d. error term ∼ (µa, σa). The firm produces the wholesale good

using capital and labor hired from the household sector at a real wage rate

wt.

Intermediate firms sell their wholesale products to retailers who trans-

form the intermediate product in a homogeneous product by application of

a CES production function. The introduction of intermediate and retail firms


50 Chapter 3

is merely a mechanical device to keep the model analytically tractable. The

CES production function is represented by:

Yt =

[∫ 1

0Yt(j)1−1/λ

pt di]1/(1−1/λ

pt )

, (3.13)

where λpt = λp + ηπ

t denotes the price mark-up, ηπt is a cost-push shock and

follows a stochastic progress of the form ηπt = ρπηπ

t−1 + επt where επ

t is an

i.i.d. error term ∼ (µπ, σπ). Retailers minimize costs,∫ ∞

0 Pt(j)Yt(j), subject

to the CES production function, (3.13). The solution to the retailers’ optimiz-

ation problem defines how the price and output of intermediary j, Pt(j) and

Yt(j), respectively, relate to aggregate prices and aggregate output Pt and

Yt, respectively. We assume that retailers compete in a perfectly competitive

market which implies that prices can be rewritten as:

Pt =

[∫ 1

0Pt(j)1−λ

pt di]1/(1−λ

pt )

. (3.14)

We adopt Calvo (1983) pricing as retailers can only change their price after

receiving a random price change signal. The exogenous probability of re-

ceiving the price signal is equal to (1− ξ p). If a retailer receives a price sig-

nal, she sets a new price denoted by Pt. If a retailer does not receive a price

signal, we allow for partial indexation. Partial indexation is done in a way

similar to wage indexation:

Pt(i) =(

Pt−1

Pt−2

)γp

Pt−1(i), (3.15)

where γp is an indexation parameter for non-optimizing firms. As a con-

sequence, prices in the model are sticky.

3.2.2 The financial side: banks

Banks act as intermediaries for all financial transactions between house-

holds and entrepreneurs. Households save deposits to smooth consumption



over time and entrepreneurs borrow to finance production. Following Gerali

et al. (2010) the banking sector is modeled as a collaboration between three

branches, i.e., a bank holding company and two retail branches: a fund-

ing branch and a lending branch. This approach ensures tractability of the

model. The two retail branches are responsible for the collection of deposits

and the allocation of loans and set interest rates in a monopolistic competit-

ive fashion. The bank holding company manages the capital position of the

banking entity.

Loan and deposit demand

Banks and borrowers often engage in long-term relationships which are vul-

nerable to asymmetric information problems. Due to this market character-

ization switching banks is considered costly, because the lender has to alloc-

ate costs to screen potential new borrowers and the borrower has to signal

creditworthiness to the new lender. The presence of switching costs due to

asymmetric information is often mentioned as a reason for market power in

the banking sector, see Diamond and Dybvig (1983), Greenbaum et al. (1989)

and Sharpe (1990).5

Market power in the banking sector is modeled by application of a Dixit-

Stiglitz framework. Each bank produces a unique variety of loans Bt(`) and

deposits Dt(`). Accordingly, loan demand by entrepreneurs and deposit de-

mand by households at bank ` are given by, see Appendix 3.A for the deriv-

ations:

Bt(`) =

(rb

t (`)

rbt

)µbt

Bt, (3.16)

5 The market structure within the banking sector is also an often cited source of marketpower. Berger et al. (2004) link market concentration to market power and the interest ratesetting behavior of banks. They find evidence that high market concentration in the bank-ing sector increases market power of banks. Other studies report limited contestability andregulatory restrictions as a source of market power, e.g. Demirguc-Kunt et al. (2004). Severalempirical papers confirm the presence of market power in the banking sector, see Bergeret al. (2004) and Degryse and Ongena (2008) for a discussion.


52 Chapter 3

Dt(`) =

(rd

t (`)

rdt

)µdt

Dt, (3.17)

where µbt = µb + ηb

t and µdt = µd + ηd

t denote the elasticity of substitution

for loans and deposits, respectively and ηbt and ηd

t are a loan demand and

deposit demand shock following a stochastic process equal to ηbt = ρbηb

t−1 +

εbt and ηd

t = ρdηdt−1 + εd

t where εbt and εd

t are i.i.d. error terms ∼ (µb, σb) and

i.i.d.∼ (µd, σd).

Bank holding company

The bank holding company operates under perfect competition and com-

bines bank capital Kbt (`) and deposits Dt(`) on the liability side and sup-

plies loans Bt(`) on the asset side to maximize its profits. Moreover, Vrt (`)

denotes the realized (superscript r) level of losses from credit defaults.

The bank holding company expects each period that a number of en-

trepreneurs default on their loan repayment because they realize an idio-

syncratic return that is too low to repay the loan. If an entrepreneur de-

faults, the bank only receives the residual claim net of monitoring costs,

(1− µ)ωt(j)rkt qt−1Kt−1(j), which happens if ωt(j) < ωt. Aggregating over

all entrepreneurs that default gives the aggregate return on loans that de-

fault: (1− µ)∫ ωt

0 ωt f (ωt)dωtrkt qt−1Kt−1. The default probability is equal to

F(ωt) and accordingly the realized amount of bank losses in period t is de-

termined by:

Vrt (`) =

(F(ωt)rb

t (`)Bt−1(`)− (1− µ)∫ ωt

0ωt f (ωt)dωtrk

t qt−1Kt−1

)ηv

t ,

(3.18)

where ηvt denotes a credit default shock. The credit default shock follows a

stochastic process ηvt = ρvηv

t−1 + εvt where εv

t is an i.i.d. error term∼ (µv, σv).

Intuitively ηvt describes the deviation of realized from anticipated losses.

Bank holding companies predict future losses based on historical informa-

tion assuming a log-normal distribution for ωt. However, during a finan-



cial crisis the log-normal distribution or the historical default losses may

not be representative for the actual default process. Consequently, actual

losses might differ from expected losses. A higher level of expected losses

increases provisioning by banks for future credit default losses which lowers

the amount of funds available for loans and raises lending rates today. A

realization of credit default losses higher than anticipated ex-ante deterior-

ates bank capital. Whereas both channels are present in the model, the credit

default shock only focuses on the latter.6

Bank holding companies determine expected default losses in the next

period, EtVrt+1(`), and reserve the equivalent today denoted by Ve

t (`) (su-

perscript e). Hence, Vet (`) = EtVr

t+1(`) and the amount of funds reserved

for future losses is based on today’s information set. Each bank holding

company has a balance sheet constraint which is given by:

Bt(`) = Dt(`) + Kbt (`). (3.19)

Bank capital, or bank equity, represents a residual claim on the bank’s profits

after having payed the debtors, operational costs and dividends:

Kbt (`) = (1− δb)Bt−1(`)− Dt−1(`) + ωb Jb

t (`) + Tt, (3.20)

where Jbt denotes overall bank profits of the retail banks and bank holding

company, (1−ωb) denotes the dividend payout ratio of the bank, δb denotes

resources used to manage the assets and Tt captures the effect of a bank

recapitalization. The precise bank recapitalization rule is specified below.

All retained earnings accumulate to bank capital and are reinvested the next

period. Using (3.19) and (3.20) it is possible to write bank capital as:

Kbt (`) = Kb

t−1(`)− δbBt−1(`) + ωb Jbt (`) + Tt. (3.21)

6 This modeling assumption is in line with existing evidence in the empirical literature onloan loss provisioning, see e.g., Laeven and Majnoni (2003) and Bikker and Metzemakers(2005) who show that credit default losses impact bank capital directly because banks do notprovision extra in good times to build a buffer for bad times.


54 Chapter 3

Moreover, the bank holding company faces a cost, denoted by the parameter

κw, whenever the value of the capital-to-assets ratio Kbt /Bt (the inverse of

the bank’s leverage ratio) deviates from the optimal capital-to-asset ratio ν.

If the capital-to-asset ratio is below the target ratio, banks are leveraged too

high and might incur insolvency costs. Insolvency costs are not explicitly

modeled because banks cannot default in our model. For this reason, we

capture the insolvency costs via the parameter κw. Without this constraint

banks would have an incentive to increase leverage indefinitely.

If the capital-to-asset ratio is above the target ratio, banks are not max-

imizing their profits as a lower ratio (higher bank leverage) would result

in higher returns. In this case, the bank’s portfolio is not on the Markowitz

frontier because banks could increase the expected return without increas-

ing volatility. In a Modigliani-Miller world a lower leverage ratio corres-

ponds to a lower risk level such that investors in the bank would require

a lower return. In this model banks cannot default. Consequently, a lower

leverage ratio does not correspond to a lower risk level which, on itself, does

not violate Modigliani-Miller. Nonetheless, banks have an incentive to max-

imize their leverage ratio and hold zero bank equity when the costs of bank

equity are higher than the cost of debt and therefore gravitate towards the

highest leverage ratio possible.

Shin (2010) shows that even if banks face bankruptcy risk, leverage tar-

geting is optimal as long as the maximum leverage ratio required by the

market absent regulation is higher than the maximum leverage ratio re-

quired by the central bank. In the real world banks have implicit govern-

ment guarantees if they are perceived “too big to fail” and depositors are

protected via deposit insurance systems. As the market is aware of these im-

plicit guarantees, leverage ratios required by the market often do not bind

because of regulatory constraints and banks have an incentive to raise their

leverage ratio.

The model does not allow banks to sell loans to other financial market

participants thereby lowering leverage contemporaneously. This assump-

tion reflects the situation in the wake of the financial crisis during which all



banks tried to sell their assets simultaneously. The interbank markets dried

up completely and prevented banks to sell their loan portfolio, usually in

the form of asset backed securities, to other market participants.

The model also does not allow banks to issue new shares. Issuing bank

equity is in general considered to be too expensive by the current share-

holders and only done by a few banks. We do not model the bank decision

to issue new equity explicitly, i.e., the model is agnostic about why the

Modigliani-Miller irrelevance proposition is violated. However, with impli-

cit government guarantees, banks can continue to operate even though the

market value of their debt is larger than the market value of their assets,

i.e., banks are effectively bankrupt. The government guarantee protects the

risk-free claim of the depositor and, as a consequence, the market value of

bank equity can still be positive. In this case, issuing new equity is indeed

expensive as it lowers the value of the implicit government guarantee and

thereby violates the Modigliani-Miller irrelevance proposition.

The bank holding company maximizes the discounted sum of the expec-

ted future cash flows by choosing the appropriate loan and deposit levels

subject to the balance sheet constraint:

maxBt(`),Dt(`)

Et

∞

∑t=0

Λpt

[(1 + rwb

t (`))Bt(`)− Bt+1(`) + Dt+1(`)−

(1 + rwdt (`))Dt(`) + ∆Kb

t+1(`)−

κw

2

(Kb

t (`)

Bt(`)− ν

)2

Kbt (`)

],

subject to Bt(`) = Dt(`) + Kbt (`), (3.22)

where Λpt is the stochastic discount rate of the bank holding company, rwd

t

and rwbt denote the deposit rate and the loan rate charged by the bank hold-

ing company to the corresponding retail branches, respectively, and ∆Kbt+1

denotes the change in bank capital. As the model is estimated in linear form,

the leverage adjustment costs are completely specified by the parameter κw.

The quadratic term is postulated for mathematical convenience. Using the


56 Chapter 3

balance sheet constraint at time t and t + 1 in the objective function, (3.22),

can be rewritten as:

maxBt(`),Dt(`)

rwb

t (`)Bt(`)− rwdt (`)Dt(`)−

κw

2

(Kb

t (`)

Bt(`)− ν

)2

Kbt (`)

. (3.23)

The FOCs link the bank holding rates on loans and on deposits to the degree

of leverage Bt/Kbt . As banks are always solvent, they are never financing

constrained and can always borrow from the central bank at rate rt. How-

ever, they cannot use these funds to increase their loan portfolio unlimitedly

as they are constrained by their leverage ratio. Arbitrage opportunities en-

sure that rwdt = rt. Using these results the FOCs can be rewritten as:

st(`) ≡ rwbt (`)− rt = −κw

(Kb

t (`)

Bt(`)− ν

)(Kb

t (`)

Bt(`)

)2

ηst , (3.24)

where ηst denotes a spread shock which follows a stochastic process ηs

t =

ρsηst−1 + εs

t where εst is an i.i.d. error term ∼ (µs, σs). Equation (3.24) links

the rate of the bank holding company to the central bank interest rate and

to bank leverage. The difference between the bank holding rate and the

risk-free rate, st, is determined by bank leverage. When expected defaults

increase, expected profits and future bank capital decline. Banks decrease

credit supply to ensure that in expectation leverage remains constant and

the spread is equal to zero. However, when the realization of defaults turns

out to be higher than anticipated, profits decline which increases leverage

contemporaneously. As a consequence, the rate set by the bank holding com-

pany increases and st can be interpreted as a credit spread that increases

(decreases) due to unanticipated firm defaults (survivals), because absent

unexpected defaults it would be constant and equal to zero.

In Bernanke et al. (1999) an increase in ωt is accounted for via an increase

of the credit spread. All losses that materialize precipitate on the real side of

the economy and are accounted for in the goods market equilibrium. While

an amplification of the downturn can be expected, leverage or balance sheet

constraints do not play a significant role. In this chapter, an increase in the



default thresholds not only increases credit spreads, but also actual defaults

which deteriorates bank capital of leveraged banks.

Retail branches

The retail branches are monopolistic competitors on both the loan and de-

posit markets. Both the lending branch as well as the funding branch pro-

duce a differentiated product and have some market power.

The lending branch maximizes its profits by lending to entrepreneurs

while financing these lending activities by borrowing from the bank hold-

ing company at rate rwbt . The lending branch maximizes its profits by choos-

ing the appropriate lending rate rbt facing quadratic interest rate adjustment

costs denoted by the parameter κb:

maxrb

t (`)

∞

∑t=0

Λpt

(rbt (`)− rwb

t (`))Bt(`)−κb

2

(rb

t (`)

rbt−1(`)

− 1

)2

rbt Bt

, (3.25)

subject to the loan demand schedule, Equation (3.16). The interest rate ad-

justment costs are introduced to mimic the empirical evidence of a slug-

gish lending rate rate pass-through (see, for example, Sørensen and Werner

(2006)).

Similarly to the lending branch, the funding branch of bank j collects de-

posits Dt(j) from households and passes these to the bank holding company

which compensates them at rate rt = rwdt (the interest rate set by the cent-

ral bank). In addition, the funding branch faces quadratic interest rate ad-

justment costs which are denoted by the parameter κd. The funding branch

maximization problem becomes:

maxrd

t (`)

∞

∑t=0

Λpt

(rt − rdt (`))Dt(`)−

κd

2

(rd

t (`)

rdt−1(`)

− 1

)2

rdt Dt

, (3.26)

subject to deposit demand, Equation (3.17). Interest rate adjustment costs

are introduced also for the funding branch to mimic the empirical evidence

of a sluggish deposit rate pass-through (Sørensen and Werner, 2006).


58 Chapter 3

Combined profits of the bank holding company, and the lending and

funding branches are equal to:

Jbt = rb

t Bt − rdt Dt −

κw

2

(qtKb

tBt− ν

)2

qtKbt −VE

t+1 + VEt −Vr

t − Cbt ,

(3.27)

where Cbt ≡

κb2

(rb

t (`)

rbt−1(`)

− 1)2

rbt Bt +

κd2

(rd

t (`)

rdt−1(`)

− 1)2

rdt Dt are the adjustment

costs for changing the interest rates at the retail level. Hence, bank profits

are determined by interest income on loans minus interest expenses on de-

posits, deviations from the optimal capital-to-asset ratio, anticipated default

losses, unanticipated default losses, and adjustment costs for changing in-

terest rates.

Aggregation and equilibrium

The goods market is in equilibrium if production equals consumption plus

the resources absorbed in the production of capital:

Yt = Ct + It + ψ(ut)Kt−1, (3.28)

where Ct ≡ CHt + CE

t . The rental market for capital is in equilibrium when

the demand for capital by entrepreneurs equals supply by capital produ-

cers: Kt =∫ 1

0 Kt(i)di. The labor market is in equilibrium when labor de-

mand by entrepreneurs equals labor supply of households and entrepren-

eurs: Lt =∫ 1

0 Lt(i)di. Finally, a conventional Taylor rule is postulated to

close the model:

(1 + rt) =(1 + r)(1−ρr)(1 + rt−1)ρr

(πtEtπt+1

π∗

)δπ(1−δr)

×(Yt

Yt−1

)δy(1−δr)

εmt , (3.29)

where εmt is a monetary policy shock which follows an AR(1) process εm

t =

ρmεmt−1 + ηm

t and ηmt is an i.i.d. error term ∼ (µm, σm). Equation (3.29) as-



sumes that the central bank has two objectives, a stable (expected) inflation

rate around the steady state inflation rate π∗ and a stable growth path de-

scribed by the deviation of Yt from Yt−1. Moreover, we assume interest rate

smoothing by the central bank and include the lagged policy rate.

For the empirical analysis in Section 3.3 we linearize the model around

the non-stochastic steady state, see Appendix 3.A for details. Throughout

the remainder of this chapter a lower case variable with a hat denotes a log-

linearized variable. It is convenient to summarize the model using matrix

notation. The reduced form of the model can be represented as:

Γ0EtZt+1 = Γ1Zt + Γ2Zt−1 + Υ0Etηt+1+ Υ1ηt, (3.30)

where Γ0, Γ1 and Γ2 are respectively the coefficient matrices specifying the

response of each observable variable at time t + 1 to all variables at time t +

1, t and t− 1, Zt =[yt, ct, it, wt, πt, bt, dt, rt, rb

t , rdt , st,

]′is a vector of observed

variables, Υ0 and Υ1 are coefficient matrices specifying the response of each

variable in Zt+1 to the vectors Etηt+1 and ηt =[ηa

t , ηvt , ηm

t , ηlt , ηi

t, ηπt , ηd

t , ηbt ,

ηct , ηi

t, ηqt]′, respectively, which contain all shocks.

3.2.3 Bank recapitalizations and countercyclical buffers

Since the global financial crisis, central banks have a wide range of instru-

ments at their disposal to alleviate stress in the banking sector. Besides, at

the height of the financial crisis, governments of advanced economies fre-

quently recapitalized banks as an emergency measure. In the current after-

math of the crisis, policy makers are in search for more structural solutions

that could potentially prevent bank recapitalizations in the future given

the potentially damaging side effects in the form of moral hazard. Among

these instruments is a countercyclical capital buffer which suggests that the

central bank tightens capital constraints during a boom and eases capital

constraints during a downturn. Bank capital constraints might induce pro-

cyclical bank behavior and countercyclical capital buffers are suggested to

alleviate this pro-cyclical nature.


60 Chapter 3

Following Paries et al. (2011) we focus on the joint determination of a

monetary policy rule and a macroprudential policy rule. We abstract from

welfare calculations and specify an ad hoc macroprudential policy rule. In

practice, countercyclical capital buffers and bank recapitalizations have a

binary structure, i.e., either the countercyclical capital buffer is activated or

the bank is recapitalized, or not. Here an endogenous rule is introduced

which is not binary but continuous. First, we introduce an endogenous policy

rule that is contingent on the ratio of credit over output which is the most

commonly used trigger variable that activates, e.g., countercyclical capital

buffers:

Myt =

(Bt

Yt− B∗

Y∗

)$y

, (3.31)

where B∗/Y∗ is the steady-state credit-to-output ratio and $y is a policy

parameter which denotes the degree to which the countercyclical capital

buffer or recapitalization is affected by changes in the credit-to-output ratio.

So, Myt is activated (My

t 6= 0) when credit-to-output differs from steady state

credit-to-output.

The credit-to-ouput ratio has been chosen as a trigger variable to activ-

ate the countercyclical buffer because it signals the economy’s ability to re-

pay its debt. A high credit-to-output ratio is informative about future credit

default losses because it might signal, for example, a bubble as credit has

expanded but output has not. The model present here, however, has no role

for inflationary bubbles. As credit is used to acquire capital for production,

credit and output grow often in accordance. Also in reality it is hard to dis-

tinguish between a bubble and an increase in credit supported by funda-

mentals. It is therefore informative to examine a more direct instrument, a

policy rule that is contingent on bank capital itself:

Mkt =

(Kb

t − Kb∗)$k

, (3.32)

where Kb∗ denotes steady state bank leverage, and $k is a policy parameter

which denotes the degree to which the countercyclical capital buffer or re-



capitalization is affected by changes in the leverage ratio. So, Mkt is activated

(Mkt 6= 0) when bank leverage differs from steady state bank leverage.

Finally, we assume that banks do not take into account the incremental

impact they have on the countercyclical capital buffer or the recapitaliza-

tion, i.e., no moral hazard is introduced in the model. The rationale for this

assumption is that each individual bank has only marginal influence on the

aggregate development of the credit-to-output ratio or the aggregate lever-

age ratio whereas the rules are only implemented at the aggregate level.

Countercyclical buffers

In reality, countercyclical capital buffers are either off and no capital sur-

charge (undercharge) is required (allowed), or they are activated and banks

are required (allowed) to hold (release), e.g., an extra percent of capital re-

lative to their assets. Countercyclical capital buffers have only an effect on

bank leverage when required bank leverage after activating the countercyc-

lical capital buffer is below the leverage ratio required by the market. Spe-

cifically, in a downturn the central bank may decide that capital buffers are

allowed to fall below the regulatory capital requirement, i.e., bank leverage

may increase. Yet, if the market requires a lower leverage ratio for solvency

reasons, an increase in the bank’s funding costs will force the bank to de-

crease leverage to a level required by the market, see for example Clerc et al.

(2015). In this case the capital requirement set by the central bank is not

binding and has no effect on credit supply.

For this reason, we might postulate that the central bank introduces a

steady state leverage ratio significantly below the market requirement in a

financial crisis. Accordingly, even after activating the countercyclical capital

buffer, the leverage ratio requirement of the central bank is still below the

market requirement. Accordingly, the leverage constraint set by the central

bank always binds, while the constraint imposed by the market never binds.

Also in practice, leverage requirements must be set at a relatively low level

to ensure that the countercyclical capital buffer binds even if financial con-

ditions deteriorate. If not, the countercyclical capital buffer has no effect as


62 Chapter 3

it is not binding.

Alternatively, the government could offer an explicit or implicit guar-

antee. This guarantee is effective if it does not jeopardize the solvency of

the government as this would increase lending rates and thereby crowd out

private investment. If the government guarantee is credible, and it does not

affect the solvency of the government, bank leverage could increase dur-

ing a downturn because the amount of bank equity required by the mar-

ket decreases. The model presented here is consistent with both interpret-

ations and simply assumes that the regulatory requirement after activating

the countercyclical capital buffer binds.

Formally, the bank leverage constraint is relaxed in the following way

when the countercyclical capital buffer is activated:

rwbt = rt − κw

(Kb

tBt− (ν + Mt)

)(Kb

tBt

)2

ηst , (3.33)

where Mt can be either Myt or Mk

t depending on which activation rule the

central bank adheres to.

Bank recapitalizations

A bank recapitalization could be designed in countless ways as a priori it

is not clear how the recapitalization should be financed. For example, the

recapitalization could be specified as a mandatory bank equity issuance, a

bail-in or a tax-financed bail-out. If the government is solvent, it could also

issue new debt to finance the bank recapitalization without affecting lend-

ing rates and private investment much. This situation might be particularly

relevant in times of a liquidity trap when the costs of debt-financed fiscal

expansions are suggested to be low (Eggertsson and Krugman, 2012). In the

model, the government could in this case recapitalize the banks and reduce

output and inflation fluctuations to zero without incurring any costs.

To analyze a less trivial trade-off, we focus on a costly recapitalization.

As the patient household in the model is both the tax-payer, bank share-

holder and depositor, any form of recapitalization is payed for by the house-



hold. If the banks issues equity or if the government recapitalizes the banks

with a loan, the patient households could loose in terms of current and/or

future consumption. Nevertheless, if Modigliani-Miller holds, the banks’

total financing costs are unaffected by their financial structure. Households

effectively convert deposits into bank equity without changing their expec-

ted claim on the banks’ future cash flow and are therefore in a risk neut-

ral setting unaffected. Households, however, might value bank equity less

than deposits for reasons of liquidity which would generate a violation of

Modigliani-Miller, see e.g. Stein (2012). For simplicity we therefore assume

that the household receives a return of zero on bank equity or a loan provided

by the government. Moreover, we analyze the case where the loan to the

bank is offered as a gift.

If the government decides on a recapitalization rather than activating

the countercyclical capital buffer, the tax Tt is set equal to the endogenous

buffer Myt or Mkb

t . In this case the government directly injects the bank with

additional capital as specified in Equation (3.21). It is therefore important to

distinguish between a countercyclical capital buffer and a recapitalization

as the former does not need funding if credible while the latter must be

financed explicitly. The taxed levied on the households is given by:

Tt = rdt Mt. (3.34)

Hence, households loose the deposit rate they would otherwise receive on

their deposits, but the principle claim on the bank remains the same. As

banks are leveraged and households hold both bank equity and deposits, a

one percent increase in bank capital yields a ν/(1− ν) percent reduction in

household deposits where ν is the leverage ratio.

3.3 Empirical methodology

In this section we specify the parameter values and the estimation strategy.

The set of parameters is divided into two partitions. Partition one contains


64 Chapter 3

parameters that control the steady state. This set of parameters entails con-

ventional parameters for which the values are taken from the literature. The

other parameter values in this set entail steady state averages which are

calibrated to reproduce steady state averages of the data set. Partition two

contains parameters that are estimated using a Bayesian estimation proced-

ure.

3.3.1 Calibrated parameters

The parameters that are conventional are categorized in partition one and

presented in the first column of Table 3.1. Their values are taken from the

literature. First, βE = 0.975 and βH = 0.994 which are also used by Gerali

et al. (2010). The share of capital in the production function α = 0.3; the de-

preciation rate of physical capital δk = 0.025; the habit parameter h = 0.7;

the coefficient of relative risk aversion σc = 1; the inverse of the elasticity

of work effort σl = 2 (see e.g., Smets and Wouters (2003) and Christiano

et al. (2005)). We set the share of inelastic entrepreneurial labor in produc-

tion Ω = 0.01 which is similar to Bernanke et al. (1999) and ensures that

entrepreneurial income has no effect on the results. The inverse of the elasti-

city of capital utilization Ψ ≡ ψ′/ψ

′′= 0.25.

The probability of default F(ω) = 3%. Bernanke et al. (1999) base this

value loosely on the United States historical average. We assume a similar

value for the euro area but experimented with higher and lower values.

These experiments showed that the model outcome is rather insensitive to

the default threshold value because it is not the steady state value that is

important but changes in the default probability and the mismatch between

what is expected and what is realized. F(ω) = 3% pins down the entrepren-

eurial physical capital-to-loan ratio (K/B) at 0.4, which is close to the his-

torical average capital-to-loan ratio of entrepreneurs.7 In this model there is

7 Assuming a log normal distribution ∼ N (0, 1) implies f (ω) ≈ 0.446 and ω ≈ 0.152.Optimization and linearization of the system results in first and second order derivativesw.r.t. Γ(ω) and µG(ω) where Γ(ωt) = F(ω) 1

2 ω2 + ω[1 − F(ω)], µG(ωt) = µF(ω) 12 ω2,

Γ′(ω) = 1 − F(ω), Γ

′′(ω) = − f (ω), G

′(ω) = µω f (ω) and G

′′(ω) = µ( f (ω) + ω f

′(ω))

which are all functions of the steady state default probability ω.



by assumption no dividend payout ωb = 1. Assuming a positive dividend

payout has no qualitative effect on the results.

The parameters representing steady state averages are calibrated based

on their historical averages. The fractions C/Y and I/Y are calibrated from

of the data series and incorporate government consumption and govern-

ment investment; wL/D is the labor income to savings ratio and is set equal

to 0.23, roughly the historical average of the data series. Following Gerali

et al. (2010) the share of entrepreneurs in the economy CE/C = 0.2. The

fractions concerning bank profit, rbB/Jb, rdD/Jb, and V/Jb are derived from

estimated parameters and therefore not calibrated, see Appendix 3.A.

Table 3.1. Calibrated parameters

Parameters Description Value

βE Discount factor entrepreneurs 0.975βH Discount factor households 0.994α Share of capital in the production function 0.300h The household habit parameter 0.700σc Relative risk aversion households 1.000σl Inverse of the elasticity of work effort 2.000δk Depreciation rate of physical capital 0.025Ω Share of households in composite labor factor 0.990Ψ = ψ

′(1)/ψ

′′(1) Capital utilization 0.250

F(ω) Probability of default 0.030C/Y Consumption to output ratio 0.780I/Y Investment to output ratio 0.220wL/D Households savings quote 0.230CE/B Consumption borrowing ratio 0.230K/B Inverse of loan to value ratio 0.400

3.3.2 Data

The model is estimated for the euro area for the period 2000:Q1-2016:Q2. The

dataset contains real economic variables: output, consumption, investment,


66 Chapter 3

hours of work, wages, outstanding loans to firms and outstanding deposits;

and price and interest variables: inflation, nominal policy rate, nominal in-

terest rate on loans, nominal interest rate on deposits and credit spreads (see

Appendix 3.B). The real economic variables are de-trended and expressed

as log-deviations from their trend. The trend value of the variables is con-

structed using the HP-filter and a smoothing parameter equal to 1600. The

prices and interest rate variables are expressed as absolute deviations from

the sample mean. Figure 3.2 shows the resulting time series.

The difference between the lending rate set by bank holding company

rwt and the policy rate rt is interpreted as a credit spread. We take credit

spread data of European firms constructed by Gilchrist and Mojon (2017)

who use individual firm level securities data to construct security-specific

credit spreads which are aggregated for the euro area to construct aggreg-

ated credit spread indicators. As the aggregate indicator is constructed from

micro level data, the spreads are, according to the authors, more informative

about aggregate credit spreads than aggregate approximations. The credit

spread data is added to be able to identify the default shock.

All real variables presented in Figure 3.2 show more or less the same pat-

tern. Output, consumption, investment, hours and wages peak before the

global financial crisis and start to decline during the global financial crisis.

Although they return swiftly to pre-crisis levels, the resurrection might also

be a characteristic of the HP-filter applied to the data series as the estim-

ated trend is not insensitive to the financial crisis. Loans show also a sharp

decline during the financial crisis and return quickly to pre-crisis levels. De-

posits show the inverse pattern. Before the global financial crisis they are at

their lowest point after which they rise steeply. The policy rate, the loan rate

and to a lesser extent the deposit rate appear to be trending downward over

the sample. Credit spreads, in contrast, appear to be trending upward; they

hit a minimum just before the start of the global financial crisis at about

5 percent points below their mean, while during the crisis they appear to

peak. The inflation rate is relatively stable over time reflecting perhaps ef-

fective monetary policy over the sample period.



3.3.3 Estimation

The second partition of parameters, containing the less conventional para-

meters, are estimated using the Bayesian estimation algorithm in Dynare.

The estimated parameters are presented in Table 3.2.

We assume that all the structural parameters follow a gamma distribu-

tion. The standard deviations are set relatively large to give the data the

opportunity to determine the value of the parameter. We follow Gerali et al.

(2010) by setting κb = 10, and κd = 10. These values ensure that the model

approximates the observed interest rate pass-through documented by the

European Central Bank (2009). Gerali et al. (2010) argue that κw is hard to

determine, for this reason they set the standard deviation equal to 5 and de-

cide on a prior value equal to 20 such that the data is able to determine this

parameter. We follow a similar approach. Setting κw = 20 implies that for

each percentage point deviation of the banks capital-to-asset ratio from the

optimal level, the interest rate spread increases by about 4 basis points. We

experimented with different values and found that the data is sufficiently

able to identify this parameter.

As µb and µd are no conventional parameters, no conventional values

are readily available. We therefore calibrate these values to ensure that they

mimic historical averages. In the Appendix Section 3.A we show that in the

steady state µb = rb∗/(rb∗− r∗) and µd = rd∗/(rd∗− r∗). These historical av-

erages are calculated by transforming the quarterly data series representing

annual rates, ry, into quarterly rates, rq, i.e. rq = exp(ln( 1+ry

4 )). Successively,

we use the historical average of these transformed loan, deposit and policy

rates to calculate µd = 4.299 and µb = 2.605. In Gerali et al. (2010) µb is calcu-

lated to be negative which implies that the deposit rate is on average below

the policy rate. Here, we find that the deposit rate is on average higher than

the policy rate. We set the costs of managing bank assets equal to δb = 0.025

close to the value chosen by Gerali et al. (2010). The optimal capital-to-loan

ratio of the bank, ν, is set equal to 8%, the capital requirement imposed by

Basel III on corporate loans.8

8 Basel III prescribes capital requirement based on the risk characteristics of the asset. The


68 Chapter 3

Following Smets and Wouters (2007) we set the partial indexation para-

meters γp and γw equal to 0.75, the probability of a price and wage update

εp = εw = 0.75 and the wage mark-up λw = 0.5. There is no consensus in

the literature regarding the value of the parameter determining the capital

adjustment costs ϕ. According to Bernanke et al. (1999), reasonable values

lie within the range 0.0− 0.5. Therefore I use a value of 0.25. Furthermore,

δy = 0.75 and δπ = 1.5 which correspond to conventional Taylor rule val-

ues. Finally, we set µ = 0.5 because the value of a credit default swap is

calculated under the assumption of a loss given default of 50%.

The prior specification of the persistence parameters and the variance of

the shocks is shown in Table 3.3. For the value of the persistence parameters

of the shocks ρι, where ι indexes a particular shock, we choose a prior value

of 0.75. As conventional, we choose a beta distribution as prior distribution

for these parameters with a standard deviation equal to 0.1. Finally, the prior

mean and variances of the shock terms are set equal to µι = 0.05 and σι =

0.005 and follow by assumption an inverse gamma distribution.

model simplifies this characteristic and only considers one asset, i.e. loans to firms, whichare homogeneous in risk and have a 100% risk weight.



Table 3.2. Table - Estimated parameters

Prior Posterior

Param. Distr. Mean S.D. Mean 10% Median 90%

κw Gamma 20.000 5.000 17.249 12.311 16.826 22.150κd Gamma 10.000 1.000 5.288 4.955 5.227 5.694κb Gamma 10.000 1.000 8.570 7.495 8.532 9.674µb Gamma 4.299 0.400 6.579 6.002 6.620 7.117µd Gamma 2.604 0.200 2.783 2.503 2.776 3.067δy Gamma 0.750 0.050 0.710 0.654 0.709 0.767δπ Gamma 1.500 0.100 1.638 1.514 1.632 1.773γp Gamma 0.750 0.250 0.276 0.190 0.273 0.370γw Gamma 0.750 0.250 0.232 0.151 0.228 0.317µ Gamma 0.500 0.100 0.419 0.326 0.422 0.509ϕ Gamma 0.250 0.100 0.110 0.088 0.110 0.133δb Gamma 0.025 0.010 0.050 0.033 0.049 0.067εp Gamma 0.750 0.050 0.835 0.819 0.836 0.850εw Gamma 0.750 0.050 0.553 0.533 0.552 0.574ν Gamma 0.080 0.005 0.093 0.085 0.092 0.100λw Gamma 0.500 0.050 0.537 0.478 0.537 0.596


70 Chapter 3

Figure 3.2. Time series plot of observable variables.

00 05 10 15-0.01

-0.005

0

0.005

0.01Policy rate: rt

00 05 10 15-10

-5

0

5#10-3 Loan rate: rb

t

00 05 10 15-2

-1

0

1

2#10-3Deposit rate: rd

t

00 05 10 15-2

0

2

4

6#10-3 Spread: st

00 05 10 15-0.01

-0.005

0

0.005

0.01In.ation: :t

00 05 10 15-0.1

-0.05

0

0.05

0.1Loans to -rms: bt

00 05 10 15-0.04

-0.02

0

0.02

0.04Deposits from households: dt

00 05 10 15-0.05

0

0.05Output: yt

00 05 10 15-0.04

-0.02

0

0.02

0.04Consumption: ct

00 05 10 15-0.1

-0.05

0

0.05

0.1Capital: it

00 05 10 15-0.02

0

0.02

0.04Hours: lt

00 05 10 15-0.04

-0.02

0

0.02

0.04Wages: wt

Notes: Interest rates, inflation and credit spreads are plotted on a quarterly basis and inabsolute deviations from the sample mean. The real variables, loans to firms, deposits tohouseholds, consumption, output, capital and hours worked, are plotted on a quarterly basisand expressed as log deviations from the HP-filtered trend.



Tabl

e3.

3.Es

tim

ated

auto

corr

elat

ion

and

stan

dard

devi

atio

npa

ram

eter

s

Para

met

ers

Labe

lD

istr

ibut

ion

Prio

rS.

D.

Mea

n10

%M

edia

n90

%

ρr

Polic

yra

tepe

rsis

tenc

eBe

ta0.

750

0.10

00.

637

0.54

50.

642

0.72

0ρ

aTe

chno

logy

Beta

0.75

00.

100

0.84

30.

798

0.84

70.

884

ρv

Def

ault

Beta

0.75

00.

100

0.64

60.

566

0.64

50.

727

ρrb

Lend

ing

rate

Beta

0.75

00.

100

0.78

00.

670

0.79

10.

870

ρrd

Dep

osit

rate

Beta

0.75

00.

100

0.29

20.

199

0.28

40.

401

ρq

Cap

ital

pric

eBe

ta0.

750

0.10

00.

727

0.68

80.

729

0.76

2ρ

sSp

read

Beta

0.75

00.

100

0.80

30.

695

0.81

20.

894

ρπ

Cos

tpus

hBe

ta0.

750

0.10

00.

327

0.23

90.

324

0.42

1ρ

lLa

bor

supp

lyBe

ta0.

750

0.10

00.

849

0.82

50.

850

0.87

2ρ

iIn

vest

men

tBe

ta0.

750

0.10

00.

664

0.57

10.

672

0.74

5ρ

cC

onsu

mpt

ion

Beta

0.75

00.

100

0.78

50.

742

0.79

00.

822

ρw

Wag

eBe

ta0.

750

0.10

00.

575

0.49

90.

576

0.65

1ρ

rnM

onet

ary

Polic

yBe

ta0.

750

0.10

00.

950

0.93

70.

950

0.96

2σ

aTe

chno

logy

Inv.

gam

0.05

00.

005

0.03

40.

031

0.03

40.

037

σv

Def

ault

Inv.

gam

0.05

00.

005

0.05

20.

045

0.05

10.

060

σ rb

Lend

ing

rate

Inv.

gam

0.05

00.

005

0.04

00.

036

0.04

00.

044

σ rd

Dep

osit

rate

Inv.

gam

0.05

00.

005

0.03

30.

030

0.03

30.

035

σq

Cap

ital

pric

eIn

v.ga

m0.

050

0.00

50.

060

0.05

30.

059

0.06

7σ

sSp

read

Inv.

gam

0.05

00.

005

0.03

80.

034

0.03

80.

041

σπ

Cos

tpus

hIn

v.ga

m0.

050

0.00

50.

042

0.03

80.

042

0.04

6σ

lLa

bor

supp

lyIn

v.ga

m0.

050

0.00

50.

046

0.04

20.

046

0.05

1σ i

Inve

stm

ent

Inv.

gam

0.05

00.

005

0.04

60.

042

0.04

60.

051

σc

Con

sum

ptio

nIn

v.ga

m0.

050

0.00

50.

047

0.04

20.

046

0.05

1σ

wW

age

Inv.

gam

0.05

00.

005

0.04

90.

043

0.04

80.

055

σ rn

Mon

etar

yPo

licy

Inv.

gam

0.05

00.

005

0.03

30.

031

0.03

30.

036


72 Chapter 3

3.4 Empirical results

Figure 3.3 and 3.4 show the prior and posterior distributions of the estim-

ated parameters and the resulting posterior mode. Table 3.2 shows the cor-

responding summary statistics. The posterior parameter values are drawn

using the Metropolis Hastings algorithm by running 5 chains of 100, 000

draws. The convergence properties of the model are assessed by means of

the convergence statistics suggested by Brooks and Gelman (1998). Over-

all, the convergence statistics indicate that the convergence properties are

satisfied, see also Adjemian et al. (2011) for the appropriate Dynare docu-

mentation.

The posterior distributions suggest that the data is informative about

most estimated parameters. In most cases the posterior distribution is sig-

nificantly different from the prior distribution. However, for λw and δy the

posterior distribution is close to the prior distribution which might indic-

ate that the data is uninformative about these parameters. To determine

whether the data is uninformative, or whether the prior value is simply

close to the value implied by the data, we experimented with different prior

values. Changing the prior mean of λw shifts the posterior distribution. Ap-

parently the data contains no information about this parameter. Fortunately,

the impulse response functions show qualitative similar results for different

values of λw. In contrast, changing δy does not affect the posterior distri-

bution much suggesting that the prior value is relatively close to the value

implied by the data.

3.4.1 Technology shock

The dynamic properties of the model are assessed by comparing the impulse

response functions resulting from a positive technology shock to the im-

pulse response functions generated by canonical DSGE models. Figure 3.5

presents the impulse response functions after a positive technology shock

represented by a one standard deviation increase in the firms’ productivity

level. The parameters are set at the estimated posterior median. In addition



Figure 3.3. Priors and Posteriors real parameters

1.2 1.7 2.20

2

4

/:

0.5 1 1.50

5

.p

0 0.5 1 1.50

5

10

.w

0.2 0.4 0.60

50

'

0.7 0.8 0.90

50

0p

0.6 0.80

10

20

0w

0.6 0.8 10

5

10/y

0.3 0.4 0.5 0.6 0.70

5

6w

Notes: Grey curve: prior; black curve: posterior; dotted line: posterior mode.

we plot the 10% and 90% credibility intervals.

In general the results are comparable to the results presented in the bench-

mark models of Smets and Wouters (2003), Christiano et al. (2005) and Gerali

et al. (2010). The technology shock increases the productivity of both capital

and labor and therefore pushes up the investment schedule and labor de-

mand. Although output increases, inflation decreases because the marginal

cost of production declines. The balance sheet of the entrepreneur extends

because capital income and the real value of physical capital increases in

value. The central bank reacts stronger to inflation than to output and de-

creases the policy rate in response to the occurrence of deflationary pressure.

Banks’ cost of funding determined by the policy rate decline and via the

monetary transmission channel both the lending and deposit rate fall. Con-

sequently, the central bank amplifies the increase in production by respond-

ing stronger to inflation than to output. The inter-temporal substitution ef-


74 Chapter 3

Figure 3.4. Priors and Posteriors financial parameters

20 40 600

0.05

5w

5 100

55b

4 6 8 10 120

0.55d

4 60

1

7b

2.5 3 3.5 40

1

2

7d

0.2 0.6 10

5

7

0.08 0.10

200

8b

0 0.02 0.04 0.060

200

400

/b

Notes: Grey curve: prior; black curve: posterior; dotted line: posterior mode.

fect causes consumption to increase, while the income effect is responsible

for the delayed increase in deposits.

Some notable difference with Gerali et al. (2010) arise due to the specif-

ics of the model presented in this chapter. Via the monetary transmission

channel, both the lending and deposit rate follow the policy rate. The differ-

ence between these two rates determines the banks’ net interest margin. The

technology shock causes the net interest margin to increase and as a result

bank capital increases. Hence, bank capital behaves procyclical which is in

line with empirical findings reported by Albertazzi and Gambacorta (2009).

In Gerali et al. (2010) bank capital is countercyclical because the banks’ in-

terest margin declines. The authors describe this result as a counter-factual

prediction of their model. Whereas the models differ both in structure and

with respect to the estimated parameters, it appears that the fall in the de-



fault probability lowers bank provisioning for credit default losses. This ap-

pears sufficient to generate procyclical bank capital dynamics. Moreover,

procyclical bank capital causes the lending rate to fall much stronger than

the deposit rate. As a result, the expansionary effect on credit supply and

investment is amplified.

Figure 3.5. Impulse response functions of a technology shock

0 5 10 15-0.5

00.5

11.5

Output: yt

0 5 10 15-0.5

00.5

11.5

Consumption: ct

0 5 10 15-1

0

1

2Investment: it

0 5 10 15

-2

0

2

Loans: bt

0 5 10 15-2

0

2Deposits: dt

0 5 10 15

-2

0

2

Bank capital: kbt

0 5 10 15-0.2

-0.1

0

0.1Policy rate: rt

0 5 10 15-2

-1

0

1Loan rate: rb

t

0 5 10 15-0.2

-0.1

0

0.1Deposit rate: rd

t

0 5 10 15-0.2

-0.1

0

0.1In.ation: :t

0 5 10 15-0.5

0

0.5Credit spread: st

Notes: Responses to a technology shock se(e Equation (3.12)) represented by the solid lineand the 10% and 90% credibility intervals are presented by the dotted lines. Prices and in-terest rates are shown as absolute deviations from their steady state, expressed in percentagepoints and real variables are percentage deviations from steady state.

3.4.2 Credit default shock

This section describes the effects of a realization of credit defaults different

from anticipated levels which is represented by a one standard deviation in-

crease in unexpected default losses. The parameters are set at the estimated


76 Chapter 3

posterior median. In addition we plot the 10% and 90% credibility intervals.

Figure 3.6 shows that, following a positive credit default shock, bank

capital falls as the funds reserved for credit default losses are insufficient

to cover the losses. The unanticipated losses deteriorate bank capital and as

a result bank leverage increases. The increase in the lending rate by banks

after a credit default shock is suboptimal from a finance perspective. The de-

cision to finance new projects should be independent from the costs made on

previous projects, i.e., losses on previous projects should be treated as sunk

costs. Credit default losses are sunk costs as these costs will be the same re-

gardless of new lending. However, Figure 3.6 shows that, even though credit

default losses are only a small fraction of the banks’ balance sheet, leverage

forces the banks to lower their lending activities substantially. These results

indicate that credit default losses affect the banks’ ability to issue new debt

and bank equity to finance new credit. Consequently, banks decrease credit

supply via an increase in the lending rate. The real side of the economy ex-

periences an increase in the lending rate and a persistent decline in credit

available for investment. Consequently, the amount of funds available for

investment in the physical capital stock declines.

The credit default shock leads to a small decrease in the inflation rate.

Firms set prices as a mark-up over their marginal costs. While demand con-

tracts and the wage rate falls, firms borrow to finance production and the

cost of borrowing increases. The net effect is a marginal decrease in the in-

flation rate on impact. The marginal decrease of inflation is consistent with

theoretical evidence presented by Christiano et al. (2005) and Gerali et al.

(2010). Moreover, Gilchrist et al. (2017) present empirical evidence for the

presence of a “cost channel” in the U.S.: when firms have weak balance

sheets, they may pass on costs increases, i.e., higher lending rates, to their

customers in the form of higher prices. These results suggest that a credit

default shock does not have much impact on inflation.

Notably, as banks are constrained by their leverage ratio, monetary trans-

mission is impeded and lending rates remain high despite monetary accom-

modation. The central bank follows a Taylor rule and lowers the policy rate



Figure 3.6. Impulse response functions of a credit default shock

0 5 10 15-0.5

0

0.5Output: yt

0 5 10 15-0.2

0

0.2Consumption: ct

0 5 10 15-1

0

1Investment: it

0 5 10 15-4

-2

0Loans: bt

0 5 10 15-2

-1

0Deposits: dt

0 5 10 15-4

-2

0Bank capital: kb

t

0 5 10 15-0.2

0

0.2Policy rate: rt

0 5 10 15-0.5

0

0.5Loan rate: rb

t

0 5 10 15-0.2

0

0.2Deposit rate: rd

t

0 5 10 15-0.05

0

0.05In.ation: :t

0 5 10 15-0.5

0

0.5Credit spread: st

Notes: Responses to a credit default shock (see Equation (3.18)) represented by the solid lineand the 10% and 90% credibility intervals are presented by the dotted lines. Prices and in-terest rates are shown as absolute deviations from their steady state, expressed in percentagepoints and real variables are percentage deviations from steady state.

because both output and inflation fall. While the increase in bank leverage

affects the lending rate directly, it does not affect the deposit rate which

closely follows the policy rate. As a result the lending rate increases while

the deposit rate falls. The decrease in the deposit rate reduces savings and

increases consumption of patient households. Entrepreneurs, however, de-

crease consumption because the lending rate has increased. Hence, monet-

ary policy only affects the recovery of household consumption while invest-

ment and entrepreneurial consumption remain subdued despite expansion-

ary monetary policy.

In conclusion, when banks are undercapitalized and cannot or will not


78 Chapter 3

issue new bank equity, monetary transmission is impeded. In this case, cut-

ting the policy rate resembles pushing a string as the banks’ cost of funds is

not the binding constraint that restricts credit supply. Decreasing the policy

rate has little direct impact. Indirectly, however, the central bank recapital-

izes the banks. The fall in the policy rate allows banks to lower their deposit

rate while the lending rate remains high. When the bank capital constraint

does not bind, arbitrage ensures that the lending rate falls in accordance

with the policy rate. However, as the entire banking sector is constrained

by their leverage ratio, the interest rate spread is not arbitraged away. Con-

sequently, the banks’ profit margin increases and banks rebuild their bank

capital from retained earnings. Lowering the policy rate thus effectively sub-

sidizes banks by taxing savers and realizes a relatively slow bank recapital-

ization.

Historical decomposition

Figure 3.7 and 3.8 show the historical decompositions of output, inflation,

consumption and investment. The historical decompositions identify a se-

quence of shocks that are able to account for the dynamics of the endogen-

ous variables and thereby provide insight in the economic impact of partic-

ular shocks. The decomposition of output shows that credit default shocks

had considerable impact on output fluctuations. In particular, during the

run-up to the global financial crisis, lower than anticipated realizations of

credit defaults drove output above potential while after the burst credit

default shocks had a noticeable adverse effect on output. The occurrence

of these credit default shocks appears largely in synchronization with the

boom-bust cycle suggesting that credit default losses have been an import-

ant determinant of historical fluctuations in output.

The historical decomposition of inflation suggests, consistent with the

interpretation of the impulse response functions above, that credit default

shocks only had minor impact on inflation dynamics. In accordance with

the pre-crisis consensus view of inflation drivers, inflation dynamics appear

mostly driven by monetary policy shocks. Another driver, although less fre-



Figure 3.7. Historical decomposition output and inflation

Notes: Horizontal axis shows years. Vertical axis shows deviations from steady state. Thevariables on the right hand side denote respectively: wage shock εw

t , investment shock εit,

labor supply shock, εlt, credit spread shock εs

t, capital price shock εlt, preference shock εc

t ,credit default shock εv

t , deposit demand shock εrdt , lending demand shock εrb

t , inflation shockεπ

t , technology shock εat , monetary policy shock εrn

t ,


80 Chapter 3

Figure 3.8. Historical decomposition consumption and investment

Notes: Horizontal axis shows years. Vertical axis shows deviations from steady state. Thevariables on the right hand side denote respectively: wage shock εw

t , investment shock εit,

labor supply shock, εlt, credit spread shock εs

t, capital price shock εlt, preference shock εc

t ,credit default shock εv

t , deposit demand shock εrdt , lending demand shock εrb

t , inflation shockεπ

t , technology shock εat , monetary policy shock εrn

t ,



quently, is the technology shock. Technology and monetary policy shocks

often cancel out indicating a relative aggressive policy response to techno-

logy shocks compared to what the conservative Taylor rule in the model

predicts. The impulse response functions in Figure 3.5 indeed suggest that

if the central bank follows a conventional Taylor rule, it does not respond

aggressively to a technology shock.

Decomposing output fluctuations in consumption and investment fluc-

tuations offers a more comprehensive assessment of the credit default shock

transmission channel. Credit default shocks appear to have had consider-

able impact on historical fluctuations in investment. In contrast, consump-

tion seems mostly unaffected by credit default shocks. These results indicate

that especially the credit supply channel of credit default shocks is relevant

for output fluctuations and supports the notion that an undercapitalized

banking sector suppresses investment.

3.4.3 Countercyclical capital buffer

When banks are undercapitalized and cannot issue new bank equity, mon-

etary transmission is impeded. Lowering the policy rate has little direct im-

pact on investment because the lending rate remains high. For this reason,

we introduce a countercyclical capital buffer to alleviate the bank capital

constraint directly. Figure 3.9 shows the response to a default shock when

the central bank implements the countercyclical capital buffer which is ac-

tivated when the credit-to-ouptut ratio differs from its steady state ratio spe-

cified by Equation (3.31). As argued before, we also assume that the coun-

tercyclical capital buffer is credible in the sense that the market does not

require a higher level of bank capital, i.e., in any case only the regulatory

capital requirement is binding.

We experimented with different values for the policy reaction parameter

$y. The solid line represents the baseline model and sets $y = 0 (no coun-

tercyclical capital buffer), the dashed line sets $y = 1 and the dotted line

sets $y = 2 while keeping all other parameters the same. The calibration res-

ults in Figure 3.9 show that the countercyclical capital buffer attenuates the


82 Chapter 3

Figure 3.9. Impulse response functions of a credit default shock and a coun-tercyclical capital buffer based on credit-to-output.

5 10 15

-0.2

-0.1

0

Output yt

5 10 15

-1.5

-1

-0.5

0Bank capital: kb

t

5 10 15

-20

-10

0

#10!3 In.ation: :t

5 10 150

0.2

0.4

0.6

0.8

Bank leverage: bt

kbt

0.15

%y = 0

%y = 1

%y = 2

Notes: prices and interest rates are shown as absolute deviations from steady state, expressedin percentage points and real variables are percentage deviations from steady state. The solidline represents the benchmark model and sets $y = 0 (no countercyclical capital buffer), thebar stripes (−−−) represents $y = 1 and the dotted line (· · · ) represents $y = 2.

fluctuations in output and inflation caused by a credit default shock. In gen-

eral, a larger response of the countercyclical buffer relative to the change in

the credit-to-output ratio attenuates macroeconomic fluctuations. Nonethe-

less, the marginal benefit is declining as can be seen by comparing the one-

for-one response ($y = 1) and the two-for-one response ($y = 2) with the

baseline model. The intuition behind this result is as follows. When credit

is used solely for investment without affecting consumption and labor sup-

ply, credit and output move one-for-one and their ratio is unaffected. How-

ever, when the bank capital constraint is relaxed by activating the counter-

cyclical capital buffer, credit supply increases by more than output because

also debt-financed consumption becomes higher. As a consequence, the ini-

tial change in the credit-to-output ratio is reduced and the marginal effect of



Figure 3.10. Impulse response functions of a credit default shock and a coun-tercyclical capital buffer based on steady state bank capital.

5 10 15

-0.2

-0.1

0

Output yt

5 10 15

-1.5

-1

-0.5

0Bank capital: kb

t

5 10 15

-20

-10

0

#10!3 In.ation: :t

5 10 150

0.5

1

Bank leverage: bt

kbt

%y = 0

%y = 0:5

%y = 0:9

Notes: prices and interest rates are shown as absolute deviations from steady state, expressedin percentage points and real variables are percentage deviations from steady state. The solidline represents the benchmark model and sets $k = 0 (no countercyclical capital buffer), thebar striped line (−−−) represents $k = 0.5 and the dotted line (· · · ) represents $k = 0.9.

the countercyclical buffer diminishes.

In reality, credit and output are potentially less correlated than in the

model. For example, credit here also accounts for mortgage loans and con-

sumer credit, while one could argue that output does not benefit directly

from these forms of credit.9 Consequently, we might observe only small

changes in the credit-to-output ratio, while in fact financial imbalances build-

up quite rapidly. It is therefore more advantageous to specify a countercyc-

lical capital buffer that is contingent on bank capital. Figure 3.10 shows the

responses to a default shock when the central bank activates the counter-

9 See for example Bernanke (2005), Mian and Sufi (2014) and Mian et al. (2016) who arguethat an increase in the household debt-to-output ratio leads to lower future output growth.In Chapters 4 and 5 we discuss these issues more extensively.


84 Chapter 3

cyclical capital buffer when bank capital differs from steady state bank cap-

ital specified by (3.32). The solid line represents the baseline model and sets

$k = 0, the bar striped line represents $k = 0.5 and the dotted line represents

$k = 0.9.

The results show that output and inflation fluctuations are further re-

duced compared to the countercyclical buffer contingent on credit-to-output.

These results are somewhat trivial as $k = 1 dissolves any feedback between

bank leverage and the lending rate and restores monetary transmission.

However, the results illustrate that countercyclical capital buffers increase

the persistence of the downturn because the deterioration of bank capital

last longer. Whereas the increase in bank leverage is precisely what the coun-

tercyclical buffer enables, it also reduces incentives to rebuild bank capital

as it reduces the costs of deviating from the capital requirement. The in-

crease in persistence is only small for output and inflation, but significant

for bank capital. Recently, Shin (2014) showed that since the global financial

crisis banks have been very slow in rebuilding bank capital and preferred

dividend payouts over the retention of earnings. The results in this chapter

indicate that activating countercyclical capital buffers in practice might fur-

ther lower bank incentives to rebuild bank capital or issue new equity. The

activation of these buffers can therefore adversely impact financial stability

in the long-run.

3.4.4 Endogenous recapitalization

A potential solution to overcome the reduced incentives to rebuild or is-

sue new bank equity is a mandatory bank recapitalization. Credit default

losses are sunk costs, but the estimation results show that credit default

shocks do affect investment. The countercyclical capital buffer analyzed in

the previous section attenuates fluctuations as it allows banks to operate at

a lower leverage ratio. However, if activated, banks take even more time

to rebuild their bank equity without accumulating any of the insolvency

costs. An endogenous recapitalization could mitigate this incentive prob-

lem as rebuilding bank equity is no longer the bank’s choice. Recapitaliza-



Figure 3.11. Impulse response functions of a default shock and a counter-cyclical capital buffer based on steady state bank leverage.

5 10 15

-0.2

-0.1

0

Output yt

5 10 15

-1.5

-1

-0.5

0Bank capital: kb

t

5 10 15

-20

-10

0

#10!3 In.ation: :t

5 10 15

-5

0

5

10

15

#10!3Bank leverage: bt

kbt

%y = 0

%y = 0:25

%y = 0:50

Notes: prices and interest rates are shown as absolute deviations from steady state, expressedin percentage points and real variables are percentage deviations from steady state. The solidline represents the baseline model and sets $kb = 0 (no countercyclical capital buffer), the barstriped line (−−−) represents $kb = 0.25 and the dotted line (· · · ) represents $kb = 0.5.

tions are effective because household deposits are effectively converted into

bank equity without changing the claim of households on the cash flows of

banks. Consequently, if the irrelevance proposition of Modigliani and Miller

(1958) holds, households and banks are unaffected by the recapitalization.

For this reason, as discussed in Section 3.2.3, we assume that households

prefer deposits over bank equity because deposits are more liquid. This as-

sumption causes a violation of the Modigliani-Miller irrelevance proposi-

tion as in Stein (2012).

As argued, the bank recapitalization can be specified in multiple ways.

Figure 3.11 shows the effects of an endogenous bank recapitalization which

is financed by the government granting the bank an interest free loan. The

recapitalization is specified by exactly the same processes as the countercyc-

lical capital buffers in the previous section. The results show that an endo-

genous recapitalization is very effective in attenuating the impact of a credit


86 Chapter 3

default shock on the real economy. Both the amplification as well as the

persistence in output and inflation fluctuations after a credit default shock

decrease substantially. These results suggest that taxing the consumers in

terms of foregone interest rate savings has only limited impact on output

and inflation. Moreover, as bank capital is supplemented when it deteri-

orates, also bank leverage remains low which increases the stability of the

financial system.

3.5 Conclusion

In this chapter we analyzed the effects of credit default losses on the bank-

ing sector and the real economy by extending a standard macro-model with

a banking sector and credit default risk. We fitted the model to euro area

data. The results show that when credit default losses are at a higher level

than anticipated—a credit default shock—bank capital deteriorates causing

bank leverage to rise and credit supply to fall. These results indicate that

banks do not issue new bank equity after a credit default shock to rebuild

their bank equity. Consequently, credit supply is constrained because banks

have a high leverage ratio. Also monetary policy is impeded because lend-

ing rates remain high despite expansionary monetary policy. Output falls

while inflation is less affected because firms set prices as a mark-up over

their marginal costs and funding costs increase. The historical decomposi-

tions show that credit default shocks are an important driver of historical

output fluctuations.

The model is able to explain the slow recovery of economic activity after

the global financial crisis despite unprecedented expansionary monetary

policy. As long as banks are undercapitalized, monetary transmission is im-

peded. Conventional monetary policy cannot invigorate credit supply in

this case because the lending rate remains high. Central banks do not lend

directly to firms and can therefore not circumvent the monetary transmis-

sion channel. The historical decompositions do indeed show that credit de-

fault shocks have been an important driver of output and investment fluctu-



ations during the recent global financial crisis. Comparable to a classic debt

overhang interpretation, credit supply is restricted because losses on exist-

ing credit restrict the issuance of new debt and new bank equity for new

credit.

Expansionary monetary policy is accommodating as it helps the banks

to recapitalize by increasing the banks’ net interest margin. However, accu-

mulating bank capital from retained earnings is a slow processes. For this

reason, we allowed for two alternative policy instruments that both address

the bank capital constraint directly. Both instruments, the countercyclical

capital buffer and the recapitalization, complement conventional monet-

ary policy and support the macroeconomic recovery. It is unclear, however,

whether both measures will be as effective in practice as they are in theory.

For one thing, we ignored the presence of moral hazard. Moreover, relaxing

leverage constraints is meaningless when the market leverage constraint be-

comes binding instead. We leave these issues for future research.

3.A Model solution

Household maximization problem

Households maximize their utility subject to their budget constraints and

labor demand. The household Lagrangian is represented by:

Lht ≡ Et

∞

∑t=0

(βH)t

ηc

t

([CH

t (i)− hCHt−1(i)

]1−σc

1− σc−

ηlt[LH

t (i)]1+σh

1 + σh

)+

λh,1t (i)

(wt(i)LH

t (i) +1 + rd

t−1

πtDt−1(i) + RPt(i)− CH

t (i)− Dt(i)

)+

λh,2t (i)

LHt (i)−

(wt(i)

wt

)− 1+λwt

λwt LH

t

, (3.A.1)


88 Chapter 3

where λh,1t (i) and λh,2

t (i) are the Lagrangian multipliers w.r.t. the budget

constraint and labor demand. The FOCs w.r.t. CHt (i), Dt(i) and LH,d

t are

given by:

ηct (C

Ht (i)− hCH

t−1(i))−σc = λh,1

t (i), (3.A.2)

Et

λh,1

t+1(i)1 + ρH

1 + rdt

πt+1

= λh,1

t (i), (3.A.3)

ηct ηl

t

[LH

t (i)]σh

= λh,2t (i)wt + λh,2

t (i). (3.A.4)

The household is represented by a labor union which can only change the

wage and sets it optimally at a level wt with a probability ξw. Otherwise, it

uses the wage indexation rule (3.4). Hence, the wage rate equals:

wt(i) =

wt(Pt−1Pt−2

)γw

wt−1(i)

if set optimally,

otherwise,(3.A.5)

To derive the household’s FOCs with respect to the wage rate in those mar-

kets where the wage rate is set optimally in the current period, we reproduce

the part of the Lagrangian that is relevant:

Lht = Et

∞

∑s=0

ηct+s(βjξw)s

−

ηlt+s[LH

t+s(i)]1+σh

1 + σh+ λt+s(i)wt+s(i)LH

t+s(i)

,

(3.A.6)

subject to labor demand LHt (i) =

(wt(i)

wt

)− 1+λwt

λwt LH

t . Substituting labor de-

mand and using εw ≡ 1+λwt

λwt

gives:

Lht = Et

∞

∑s=0

(βjξw)s

−

ηlt+s

1 + σh

[(wt+s(i)

wt+s

)−εw

LH,dt+s

]1+σh

+



λt+s(i)(

Pt

Pt−1

)γw(

w1−εwt+s (i)wεw

t+s

)LH,d

t+s

. (3.A.7)

Taking the derivative w.r.t. wt gives

w1+εwσht (i)

∞

∑s=0

ηct+s(βjξw)s LH,d

t+s(CHt+s(i)− hCH

t+s−1(i))−σc

(1 + λwt )

=

Et

∞

∑s=0

(βjξw)s(

ηlt+s

[LH,d

t+s

]σhwεwσh

t+s

), (3.A.8)

and using that s periods after the optimization wt+s =(

Pt+sPt+s−1

)γwwt+s−1 and

rewriting (3.A.8) gives:

wt(i)Pt

Et

∞

∑s=0

βs(ξw)s

(

PtPt−1

)γw

Pt+sPt+s−1

LHt+s(C

Ht+s(i)− hCH

t+s−1(i))−σc

1 + λw−

(ηl

t+s

[LH,d

t+s

]σh)

= 0.

(3.A.9)

Using the wage indexation rule, it is possible to write the aggregate wage

process as:

W− 1

λwt = ξw

((Pt−1

Pt−2

)γw

Wt−1

)− 1λw

+ (1− ξw)w− 1

λwt . (3.A.10)

Entrepreneur maximization problem

Entrepreneurs maximize their utility subject to the budget constraint, the

participation constraint of the banks and the capital accumulation identity:

Let ≡Et

∞

∑t=0

ηct (βE)t

ln

CEt − hCE

t−1

+

λet

([1− Γ(ωt+1)]

[rk

t+1ut − ψ(ut)]

Kt + Bt−


90 Chapter 3

1 + rbt−1[1− Γ(ωt)]

πtBt−1 − It − wtLH

t − CEt

)+

λet φt

([Γ(ωt+1)− µG(ωt+1)]rk

t+1utqtKt −rwb

tπt+1

Bt

)+

λetqt

((1− δk)Kt−1 +

[1− ψ

(ηi

t It

It−1

)]It − Kt

)(3.A.11)

where wt =(

wHt

Ω

)Ω ( wEt

1−Ω

)1−Ω. The FOCs w.r.t. CE

t , Kt, Bt, ωt+1, It and ut,

using the bank participation constraint with equality denote:10

ηct

CEt − hCE

t−1= λe

t , (3.A.12)

([1− Γ(ωt+1)](rk

t+1ut − ψ(ut))− qt

)+

λet+1

λet

βEqt+1(1− δk)+

φt

([Γ(ωt+1)− µG(ωt+1)]rk

t+1utqt

)= 0, (3.A.13)

λet+1βE 1 + rb

t [1− Γ(ωt+1)]

πt+1+ φtλ

et

rwbt

πt+1= λe

t , (3.A.14)

Γ′(ωt+1)(rk

t+1ut − ψ(ut)) =φt[Γ′(ωt+1)− µG

′(ωt+1)]rk

t+1utqt+

λet+1

λet

rbt Γ′(ωt+1)

πt+1

Bt

Kt(3.A.15)

λet qt

([1− ψ

(ηi

t It

It−1

)− ψ

′(

ηit It

It−1

)ηi

t It

It−1

]− 1)+

λet+1qt+1ψ

′(

ηit It

It−1

)(ηi

t It

It−1

)(It

It−1

)= 0, (3.A.16)

10 We assume free entry and exit in the banking sector such that competition equalizes thelending rate to the weighted average cost of funding.



[1− Γ(ωt+1)](rkt+1 − ψ

′(ut))Kt + φt[Γ(ωt+1)− µG(ωt+1)]rk

t+1qtKt = 0.

(3.A.17)

and the three constraints stated in (3.A.11).

Firms maximization problem

Retailers buy the intermediate products produced in the intermediate goods

sector and transform it into a homogeneous good Yt using a CES production

function, see Dixit and Stiglitz (1977):

Yt =

[∫ 1

0Yt(j)1−1/λp di

]1/(1−1/λp)

, (3.A.18)

where Yt(j) is an unique input variety produced by entrepreneur j and λp

is the elasticity of substitution in production. The retailer minimizes costs∫ ∞0 Pt(j)Yt(j) subject to the CES production function, Equation (3.A.18). Hence,

the retailer optimization problem becomes:

Lt ≡∫ 1

0Pt(j)Yt(j)di + λt

[Yt −

[∫ 1

0Yt(j)1−1/λp di

]1/(1−1/λp)]

. (3.A.19)

The solution defines unit costs Pt and demand for Yt(j):

Pt ≡[∫ 1

0P1−λp

t di]1/1−λp

, (3.A.20)

Yt(j) =Yt

[Pt(j)

Pt

]−λp

. (3.A.21)

Entrepreneurs own firms therefore the maximization problem of firm i is

part of the entrepreneurs decision problem. From Equation (3.12) we derive

the intermediate firm optimization problem. This is an intermediate step to

determine the optimal capital-labor mix:

minKt(i),LH

t (i)rk

t Kt(i) + WtLHt (i),


92 Chapter 3

subject to Yt(i) = At[Kt(i)αLHt (i)

1−α]. (3.A.22)

Cost minimization gives the following optimal capital-labor condition:

WtLHt (i)

rkt Kt(i)

=1− α

α, (3.A.23)

which implies that the capital-labor ratio is identical across firms. Firms’

marginal costs are given by:

MCt =1At

(rk

tα

)α( Wt

1− α

)1−α

, (3.A.24)

where MCt denotes the intermediate firms’ marginal costs. Firms maximize

expected firm value by setting prices Pt(i):

Πt(i) ≡NPt(i)

Pt=

[Pt(i)

Pt− MCt

Pt

]Yt

(Pt(i)

Pt

)−λpt

. (3.A.25)

Firms maximize their real profits Πt(i) by choosing the price level Pt(i). Us-

ing Calvo Pricing (Calvo, 1983), and denoting the probability that a firm is

able to change its price by the probability (1− εp), we obtain the expected

value of the firm that has just received a “green light”, i.e., the firm is al-

lowed to change its price in period t, and has set a new price Pnt (i):

maxPn

t (i)Et

∞

∑s=0

(εp)sβE[

Pnt (i)

Pt+s− MCt+s

Pt+s

]Yt+s

(Pn

t (i)Pt+s

)−λpt

. (3.A.26)

Maximizing Equation (3.A.26) w.r.t. the new price Pnt (i) and rewriting gives:

Pnt (i) = Pn

t =λ

pt

λpt − 1

Et∑∞

s=0(εp)sβEPλ

pt

t+sYt+sMCt+s

Pt+s

∑∞s=0(ε

p)sβEPλpt −1

t+s Yt+s

. (3.A.27)



As standard, the law of motion of the price level is given by:

(Pt)1−λ

pt = ξ p

((Pt−1

Pt−2

)γp

Pt−1(i))1−λ

pt

+ (1− ξ p)(Pnt )

1−λpt . (3.A.28)

Finally, firms do not incorporate the marginal effect they have on the

aggregate probability of default of all firms. Besides, households perfectly

diversify between all the firms in the economy. The law of large numbers

ensures that the representative households receives real dividend payments

equal to:

Πt = [1− F(ω)]

[1− MCt

Pt

]Yt. (3.A.29)

Banks

Loan and deposit demand

The demand function for loans is derived in a similar fashion as demand for

product Yt(i). Entrepreneurs minimize their loan payments subject to the

aggregation technology, see Dixit and Stiglitz (1977):

Lbt ≡

∫ 1

0rb

t (j)Bt(j)dj + λbt

[Bt −

[∫ 1

0Bt(j)1−1/µb dj

]1/(1−1/µb)]

. (3.A.30)

Solving this problem by aggregating all FOCs across all entrepreneurs gives

loan demand at bank j:

Bt(j) =(

rbt (j)rb

t

)µb

Bt. (3.A.31)

In a similar fashion the deposit demand function is derived. Households

maximize interest revenues from deposits subject to the aggregation tech-

nology:

Ldt ≡

∫ 1

0rd

t (j)Dt(j)dj + λdt

[Bt −

[∫ 1

0Dt(j)1−1/µd dj

]1/(1−1/µd)]

. (3.A.32)


94 Chapter 3

Solving this problem by aggregating all FOCs across all household gives

deposit demand at bank j:

Dt(j) =(

rdt (j)rd

t

)µd

Dt. (3.A.33)

Retail Branch

The retail branch of bank j consists out of 2 parts, a lending branch and a

funding branch. Both maximize their profits subject to the demand sched-

ules by choosing the appropriate interest rates. Substituting demand for

loans, Equation (3.16), in Equation (3.25) gives the following maximization

problem:

maxrb

t (j)

∞

∑t=0

λh,1t

(rbt (i)− rwb

t )

(rb

t (j)rb

t

)µb

Bt −κb

2

(rb

t (j)rb

t−1(j)− 1

)2

rbt Bt

,

(3.A.34)

The solution to the problem is:

(rb

t (j)rb

t

)µb

Bt

((1 + µb)− µb rwb

t

rbt (j)

)+ κb

(1

rbt−1(j)

− rbt (j)

(rbt−1(j))2

)rb

t Bt+

κbβHt

λh,1t+1

λ1,ht

Et

(rb

t+1(j)rb

t (j)− 1

)(rb

t+1(j)rb

t (j)

)2

Bt+1

= 0.

(3.A.35)

The solution to the lending branch optimization problem, dropping the bank

indexation parameter ` which imposes a symmetric equilibrium (rbt (j) ≡ rb

t ,

∀j), yields:

−κb

[(1− rb

t

rbt−1

)rb

t

rbt−1

+βHt

λh,1t+1

λ1,ht

Et

(rb

t+1

rbt− 1)(

rbt+1

rbt

)2 Bt+1

Bt

]=

1− µb + µb rwbt

rbt

, (3.A.36)



where λh,1t denotes the multiplier on the patient household budget con-

straint (3.3). Notice that if Equation (3.A.36) is log-linearized we obtain Equa-

tion (3.A.56).

In a similar fashion the funding branch maximizes its profits subject to

the deposit demand schedule. Substituting demand for deposits, Equation

(3.17), in Equation (3.26) gives the following maximization problem:

maxrd

t (j)E0

∞

∑t=0

λh,1t

(rt − rdt (j))

(rd

t (j)rd

t

)µd

Dt −κd

2

(rd

t (j)rd

t−1(j)− 1

)2

rdt Dt

.

(3.A.37)

The solution, after rewriting in a similar fashion as in Equation (3.A.35), is:

(rd

t (j)rd

t

)µd

Dt

(− 1 + µd − µd rt

rdt (j)

)+ κd

[(1

rdt−1(j)

− rdt (j)

(rdt−1(j))2

)rd

t Dt

+ βHt

λh,1t+1

λ1,ht

Et

(rd

t+1(j)rd

t (j)− 1

)(rd

t+1(j)rd

t (j)

)2

Dt+1

]= 0. (3.A.38)

The solution to the funding branch optimization problem, dropping the

bank indexation parameter ` which imposes a symmetric equilibrium (rdt (j)

≡ rdt , ∀j), yields:

κd

[(1− rd

t

rdt−1

)rd

t

rdt−1

+ βHt

λh,1t+1

λ1,ht

Et

(rd

t+1

rdt− 1)(

rdt+1

rdt

)2 Dt+1

Dt

]=

1− µd + µd rt

rdt

. (3.A.39)

The log-linear model

For the empirical analysis we linearize the model around the non-stochastic

steady state. A hat denotes a log-linearized variable. The household con-

sumption Euler is obtained by combining (3.A.3) and (3.A.2) in linearized


96 Chapter 3

form represented by:

cHt =

h1 + h

cHt−1 +

11 + h

EtcHt+1 −

1− h1 + h

(rd

t − Etπt+1)+

1− h1 + h

(ηct − Etηc

t+1) . (3.A.40)

This is the conventional forward-looking consumption equation with ex-

ternal habit formation, i.e., consumption today depends on past consump-

tion and expected consumption.

Linearizing the wage setting equation, (3.A.9) and (3.A.10), gives:

wt =βH

1 + βH

(Etwt+1+ Etπt+1+

1βH wt−1

)− 1 + βHγw

1 + βH πt+

γw

1 + βH πt−1 −1

1 + βH(1− βHεw)(1− εw)(

1 + (1+λw)σlλw

)εw

×

(wt − σl lH

t −1

1− h(cE

t − cEt−1)− ηl

t

). (3.A.41)

The wage rate depends via partial indexation positively on the past wage

rate and via Calvo pricing positively on the expected future wage rate .

The entrepreneur consumption Euler is given by combining (3.A.12) and

(3.A.14). Linearizing both equations yields:

− 11− h

cEt +

h1− h

cEt−1 + ηc

t = λet , (3.A.42)

and (λe

t+1 + rbt − πt+1

)−(

1[1− Γ(ω)]

)Γ′(ω)ω ˆωt+1+(

φrb

1− φrb

)(φt + λe

t + rwbt − πt+1

)= λe

t , (3.A.43)

where

rb = (1− βE)βE[1− Γ(ω)] + φ (3.A.44)



and

φ =

(Γ′(ω)

[Γ′(ω)− µG′(ω)]

)(1− rb

rkBK

)(3.A.45)

where ω = rbB/rkK. Consumption of the entrepreneur evolves in an sim-

ilar fashion as consumption of the households; it depends on past and on

expected consumption. However, entrepreneurial consumption depends, in

contrast to households consumption, on the real lending rate rather than

the real deposit rate. Moreover, the probability of default also affects the

consumption decision of the entrepreneur.

The investment equation (3.A.16) is standard and in linearized form rep-

resented by:

it =1

1 + βE it−1 +βE

1 + βE Etit+1+1

1 + βE1ϕ

qt +1

1 + βE ηit−

βE

1 + βE Etηit+1, (3.A.46)

where ϕ = ψ′′. Investment depends on past and expected investment via

the capital adjustment costs function.

The capital pricing equation (3.A.13) is linearized and represented by:

qt =[1− Γ(ω)]rk rkt+1 + [1− Γ(ω)]

(rk − ψ

′(u))

ut+

βE(1− δk)(λe

t+1 − λet + qt+1

)+

[Γ(ω)− µG(ω)]φrk(

φt + rkt+1 + ut + qt

), (3.A.47)

where

rk =1− βE (1− δk)

[1− Γ(ω)] + φ[Γ(ω)− µG(ω)](3.A.48)

which is higher than the steady state return to capital in Smets and Wouters

(2003) because firms need to pay banks a mark-up for the possibility of bank-

ruptcy.


98 Chapter 3

Linearizing the FOC for the default threshold (3.A.15) gives:

Γ′′(ω)(rk − ψ(1))ω ˆωt+1 + Γ

′(ω)rk

(rk

t+1 + ut

)=

[Γ′(ω)− µG

′(ω)]rkφ

(φt + rk

t+1 + ut + qt

)+

[Γ′′(ω)− µG

′′(ω)]rkφω ˆωt+1+

rbΓ′(ω)

b∗

k∗(

λet+1 − λe

t+1 + rbt − πt+1 + bt − kt

)+ rbΓ

′′(ω)

b∗ωk∗

ˆωt+1,

(3.A.49)

where lower case letters with a star (∗) denote steady state values. Moreover,

(3.A.49) argues that both a lower return to capital, a lower payback prob-

ability of the loan and the bank participation constraint affect the defaults

threshold. Linearizing the FOC for the utilization rate (3.A.17) gives:

[1− Γ(ω)][rk

t rkt+1 + ψ

′′(u)ut

]− Γ

′(ω)(rk − ψ

′(u))ω ˆωt+1+

[Γ(ω)− µG(ω)]rkφ(

φt + rkt+1 + qt

)+ rkΓ

′(ω)ω ˆωt+1 = 0, (3.A.50)

which is different from Smets and Wouters (2003) because in this model the

probability of default interacts with the capital utilization rate. Linearizing

the bank participation threshold (3.11) gives:

[Γ′(ω)− µG

′(ω)]

[Γ(ω)− µG(ω)]ω ˆωt+1 =

(rwb

t − πt+1 + bt

)−(

rkt+1 + qt + kt + ut

),

(3.A.51)

which states that the default threshold is at the aggregate level determined

by aggregate entrepreneurial leverage.

The model of the production side of the economy is standard. The Cobb-

Douglas production function is represented by:

y = at + αkt−1 + αψrkt + (1− α)lt. (3.A.52)



The optimal capital labor condition is given by:

lHt = −wt + rk

t + kt−1, (3.A.53)

and the inflation rate is given by:

πt =βE

1 + βEγpEtπt+1+

γp

1 + βEγpπt−1+

11 + βEγp

(1− βEεp)(1− εp)

εp(αrk

t + (1− α)wt − ηat + η

pt ).

(3.A.54)

The financial side of the economy is represented by the lending rate set

by the bank holding company:

rwbt − rt =−

κwν3

r(kb

t − bt). (3.A.55)

Hence, the spread between the lending rate set by the bank holding com-

pany and the risk-free rate (rwbt − rt) can be either positive or negative de-

pending on leverage. If, for example, leverage is low such that the capital-

to-asset ratio is above the optimal capital-to-asset ratio ν, bank capital kbt is

sufficient to cover the outstanding loans bt. The interest spread will have to

rise to decrease the amount of outstanding loans.

Log-linearizing the loan rate setting equation gives:

rbt = ζb

1rbt−1 + ζb

2Etrbt+1+ ζb

3rwbt , (3.A.56)

where ζb1 ≡ κb/(µb − 1 + (1 + βH)κb), ζb

2 ≡ βHκb/(µb − 1 + (1 + βH)κb),

ζb3 ≡ (µb − 1)/(µb − 1 + (1 + βH)κb). Equation (3.A.56) states that the loan

rate depends on the loan rate in the previous period, the expected loan rate

in the next period and the borrowing costs charged by the bank holding

company. If the loan rate is perfectly flexible (κb = 0), the maximization

problem simplifies to rbt = rwb

t µb/(µb − 1) and rbt = rwb

t . Hence each branch

simply sets the loan rate as a mark-up over its marginal costs. Note that


100 Chapter 3

default losses do not affect the optimization problem of the retail branch, but

they do affect the rate set by the bank holding company, rwbt , bank holding

companies charge their retail branches. Hence, an increase in default losses

does affect rbt via an increase in rwb

t .

The solution to the funding branch optimization problem is:

rdt = ζd

1 rdt−1 + ζd

2Etrdt+1+ ζd

3 rt, (3.A.57)

where ζd1 ≡ κd/(µd + 1 + (1 + βH)κd), ζd

2 ≡ βHκd/(µd + 1 + (1 + βH)κd),

and ζd3 ≡ µd + 1/(µd + 1 + (1 + βH)κd). Similar to the lending branch, the

deposit rate depends on the deposit rate in the previous period, the deposit

rate in the coming period, and the lending rate offered by the bank holding

company. If the deposit rate is perfectly flexible (κd = 0) the maximization

problem simplifies to rdt = rtµd/(µd − 1) and rd

t = rt.

The central bank stabilizes the economy via a simple Taylor rule:

rt =δr rt−1 + (1 + r)(1− δr)δπ(πt + Etπt+1)+

(1 + r)(1− δy)δr(yt − yt−1) + ηmt . (3.A.58)

All that remains is the evolution of the state variables and the goods market

equilibrium that closes the model. The capital accumulation identities are:

kt =δk it + (1− δk)kt−1, (3.A.59)

kbt =kb

t−1 −δbb∗

kb∗ bt−1 +jb∗

kb∗ jbt +

t∗

kb∗ tt, (3.A.60)

where in steady state δbb/kb∗ = jb/kb∗ = δb/ν and we set t∗/kb∗ = δb/ν, i.e,

the bank recapitalization is added to bank profits.

As the changes in deposits and bonds are important for leverage in the

banking sector, these variables are modeled explicitly via the budget iden-

tities of the households and the entrepreneurs:

dt =(1 + rd)dt−1 + rdt−1 − πt +

w∗lh∗

d∗(wt +

ˆlHt − tt) +

rp∗

c∗rpt−



cH∗

d∗cH

t , (3.A.61)

and

bt =−rkk∗

b∗([1− Γ(ω)]

(rk

t+1 + kt

)− Γ(ω)ω ˆωt+1

)+(

1 + rb[1− Γ(ω)])

bt−1 + [1− Γ(ω)]rb(

rbt−1 − πt

)−

Γ′(ω)rbω ˆωt+1 +

i∗

b∗it +

wlH∗

b∗(

wt + LHt + tt

)+

cE∗

b∗cE

t . (3.A.62)

As t∗ is in steady state equal to zero, we simply subtract the lump-sum tax

from labor income. Bank profits and expected credit default losses are rep-

resented by:

jbt =

rb

δb (bt + rbt )−

rd (1− ν)

δb (dt + rdt )−

rd (1− ν)−(δb − rb)

δb (vt + Etvt+1 − Et−1vt), (3.A.63)

and

vt =ξv∗(rbt + bt) + (1− ξv∗)(rk

t+1 + qt + kt)−

ξv∗(

f (ω)ω

2+ F(ω)

)ˆωt + ηv

t , (3.A.64)

where

ξv∗ ≡ F(ω∗)b∗rb∗

F(ω∗)b∗rb∗ − (1− µ)∫ ω∗

0 ω∗ f (ω∗)dω∗rk∗k∗

=F(ω∗)[Γ(ω∗)− µG(ω∗)]

F(ω∗)[Γ(ω∗)− µG(ω∗)]− (1− µ)G(ω∗). (3.A.65)

We used the steady state conditions for bank profits jb∗ = rbb∗ − rdd∗ − v∗,

bank capital accumulations δbb∗ = jb∗, bank balance sheet b∗ = d∗+ kb∗ and

kb∗/b∗ = ν. These conditions give 1− ν = d∗/b∗ and v∗/b∗ = rd (1− ν)−


102 Chapter 3

(δb − rb). The model is closed by the goods market equilibrium condition:

yt =

(1− δk k∗

y∗

)ct + δk k∗

y∗it. (3.A.66)

Linearization of the countercyclical capital buffers yields:

myt = $y

(bt − yt

), (3.A.67)

mkb

t = $kb

(kb

t

), (3.A.68)

and once activated the lending rate set by the bank holding company is

determined by the whole sale bank as:

rwbt − rt =−

κwν3

r(kb

t − bt − myt ), (3.A.69)

or

rwbt − rt =−

κwν3

r(kb

t − bt − mkb

t ), (3.A.70)

depending on which activation rule the central bank applies.

3.B Variables

Consumption: Final consumption aggregates - Current prices seasonally

adjusted and adjusted data by working day in millions of euros. Source:

Eurostat.

Output: GDP and main components - Current prices seasonally adjusted

and adjusted data by working day in millions of euros. Source: Eurostat.

Investment: Gross fixed capital formation - Current prices seasonally adjus-

ted and adjusted data by working day in millions of euros. Source: Eurostat.

Wages: Gross wages and salaries seasonally adjusted and adjusted data by



working day in millions of euros. Source: Eurostat.

Price inflation: Harmonized Index of Consumer Prices (2005=100) monthly

data. Source: Eurostat.

Nominal policy rate: Money market interest rates - monthly data (day-to-

day) Eurostat.

Outstanding loans to firms: Euro area (changing composition), Outstand-

ing amounts at the end of the period (stocks), MFIs excluding ESCB re-

porting sector - Loans, Total maturity, All currencies combined - Euro area

(changing composition) counterpart, Non-Financial corporations (S.11) sec-

tor, denominated in Euro, data neither seasonally nor working day adjusted.

Source: European Central Bank Statistical Data Warehouse.

Outstanding deposits to households: Euro area (changing composition),

Outstanding amounts at the end of the period (stocks), MFIs excluding ESCB

reporting sector - Overnight deposits, Total maturity, All currencies com-

bined - Euro area (changing composition) counterpart, Households and non-

profit institutions serving households (S.14 & S.15) sector, denominated in

Euro, data neither seasonally nor working day adjusted. Source: European

Central Bank Statistical Data Warehouse.

Nominal interest rate on loans: Euro area (changing composition), Annu-

alised agreed rate (AAR) / Narrowly defined effective rate (NDER), Credit

and other institutions (MFI except MMFs and central banks) reporting sector

- Loans other than revolving loans and overdrafts, convenience and exten-

ded credit card debt [A20-A2Z], Over 1 and up to 5 years initial rate fixa-

tion, Over EUR 1 million amount, New business coverage, Non-Financial

corporations (S.11) sector, Euro. Source: European Central Bank Statistical

Data Warehouse.


104 Chapter 3

Nominal interest on deposits: Euro area (changing composition), Annual-

ised agreed rate (AAR) / Narrowly defined effective rate (NDER), Credit

and other institutions (MFI except MMFs and central banks) reporting sec-

tor - Deposits with agreed maturity, Up to two years original maturity, New

business coverage, Households and non-profit institutions serving house-

holds (S.14 and S.15) sector, Euro. Source: European Central Bank Statistical

Data Warehouse.

Credit risk: the credit risk indicator is constructed by Gilchrist and Mojon

(2017).


Chapter 4

Mortgage loans and shadow

banks

4.1 Introduction

Since the 1980s the banking sector has been characterized by three major

trends. Perhaps the best documented trend is the secular decline in (real)

interest rates, see Figure 4.1. In March 2005 former Fed chairman Bernanke

emphasized the existence of a global savings glut, an increase in the global

supply of savings, as the main source of this decline in interest rates.1 An

efficiently functioning banking sector allocates these savings to their most

productive use. However, starting in the 1980s and up to the recent global

financial crisis a second trend is observed. Banks increased the amount of

loans secured by real estate, henceforth mortgages, much faster than the

amount of commercial and industrial loans, henceforth corporate loans, see

Figure 4.2. This reallocation of bank lending was accompanied by a third

trend: a shift from regulated banking towards unregulated banking (hence-

forth: shadow banking), see Figure 4.3.

There is a clear correlation between the growth of shadow bank liabil-

1 Bernanke (2005) argues that developing countries increased their savings rate by decreas-ing their consumption. These savings were subsequently used to buy assets from developedcountries which put downward pressure on their interest rates. See also Caballero et al.(2008) for a more detailed analysis of the decline in real interest rates.


106 Chapter 4

ities and the growth rate of mortgage loans, see Figure 4.4. However, no

encompassing framework exists that describes a causal relationship in a

general equilibrium context as these trends have, typically, not been con-

sidered together. Nevertheless, recent concerns regarding financial stability

imply that such a framework is needed. These concerns arise because, on

the one hand, a reallocation of lending towards housing investment rather

than physical capital formation might harm the economy’s production capa-

city, making it eventually harder to repay mortgage debt. A vastly growing

shadow banking sector, on the other hand, might increase the likelihood of

fire-sales and bank runs.2 This chapter builds a tractable model that shows

how an exogenous inflow of deposits on bank balance sheets depresses real

interest rates economy-wide and increases the share of mortgages on the ag-

gregate bank balance sheet. This in turn fosters growth of, in particular, the

shadow banking sector.3 In doing so, we show that growth of the shadow

banking sector reduces financial stability because shadow banks create more

uninsured deposits than socially optimal.

The intuition behind the relative reallocation of bank lending from cor-

porate loans to mortgage loans is as follows. The model distinguishes two

assets that can serve as collateral for bank loans: houses for mortgages and

physical capital for corporate loans. By assumption the assets differ with

respect to their supply elasticity; on average the supply of physical capital

is more elastic than the supply of houses. An exogenous inflow of depos-

its on bank balance sheets depresses interest rates and induces impatient

households to demand more credit for both houses and physical capital. In-

elastic housing supply relative to the supply of physical capital causes house

2 For example Bernanke (2005) argues that in the long run housing adds less to productivitygrowth than productive capital. Mian and Sufi (2014) and Mian et al. (2016) show that anincrease in the household debt-to-GDP ratio predicts lower GDP growth and higher unem-ployment in the succeeding periods. Gennaioli et al. (2013) show how an exogenous increasein savings drives securitization, leverage and financial instability in the shadow banking sec-tor. Moreira and Savov (2014) examine the interaction between shadow banks and the realeconomy and show how shadow banks can create liquidity via securitization but also addi-tional instability.

3 Thereby the model also provides a theoretical explanation for the empirical findings ofJorda et al. (2015) who show that the rise in mortgage debt was closely associated with loosemonetary policy.


Mortgage loans and shadow banks 107

Figure 4.1. Up and downward sloping trend in effective federal funds rate

0

2

4

6

8

10

12

14

16

18

20

1957 1962 1967 1972 1977 1982 1987 1992 1997 2002 2007 2012 2017

Per

cen

tag

e p

oin

ts

Time (years)

Recession Effective Federal Funds Rate

The effective federal funds rate is the interest rate at which depository institutions tradefederal funds (balances held at Federal Reserve Banks) with each other overnight. Source:Federal Reserve Bank of St. Louis database (FRED Economic Data).

Figure 4.2. Real estate and corporate loans as share of U.S. financial sector

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

1934 1942 1950 1958 1966 1974 1982 1990 1998 2006 2014

Rel

ati

ve

to t

ota

l fi

na

nci

al

ass

ets

Time (year)

Recessions Loans secured by real estate Commerical and industrial loans

Notes: The blue line denotes loans secured by real estate (predominately mortgage loans).The red line denotes commercial and industrial loans (corporate loans). Both as a share of thetotal amount of financial assets of the domestic financial sector in the U.S. Source: Historicalstatistics on banking (Federal Deposit Insurance Corporation).


108 Chapter 4

Figure 4.3. Assets regulated and shadow banks as % of U.S. financial sector

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

1957 1962 1967 1972 1977 1982 1987 1992 1997 2002 2007 2012 2017

Rel

ati

ve

to T

ota

l F

ina

nci

al A

sset

s

Time (years)

Recession Fraction of Shadow Banks Fraction of Regulated Banks

Notes: The blue line shows the total liabilities of private depository institutions (regulatedregulated banks). The red line shows other financial intermediaries except insurance com-panies and pension funds (unregulated shadow banks). Both as a share of the total amountof financial assets in the U.S. Source: Flow of funds accounts of the United States (FRB).

Figure 4.4. Growth of mortgage loans and shadow bank liabilities U.S.

-15%

-10%

-5%

0%

5%

10%

15%

20%

25%

30%

35%

1957 1962 1967 1972 1977 1982 1987 1992 1997 2002 2007 2012 2017

Yea

r-o

n-Y

ear

cha

ng

es (

%)

Time (years)

Recession Growth Shadow Bank Assets Growth Mortgage Loans

Notes: the red lines shows the growth rate of other financial intermediaries (unregulatedshadow banks). The blue line shows the growth rate mortgage loans. Correlation 0.69.Source: Author’s own calculations using data from the Flow of funds accounts of the UnitedStates and Federal Reserve Bank of St. Louis database.



prices to rise relative to the price of physical capital. The value of collateral

for mortgage loans increases relative to the value of collateral for corporate

loans. Consequently, banks increase mortgage lending relative to corporate

lending. Hence, collateral with a low supply elasticity shows more price and

credit supply fluctuations than collateral with a high supply elasticity.

After having established a relationship between an inflow of deposits

and a relative increase in mortgage lending, we show how this relation-

ship can foster growth of, in particular, the shadow banking sector. In the

model, both regulated and shadow banks can create safe money-like claims

(deposits) which allows them to extract a rent from households, see, e.g.,

Gorton and Pennacchi (1990), Stein (2012) and Krishnamurthy and Vissing-

Jorgensen (2015). To keep deposits perfectly safe and liquid in any state of

the world, regulated banks are compelled to buy deposit insurance. As in

Stein (2012) and Hanson et al. (2015), shadow banks are not compelled to

participate in the deposit insurance scheme. To create ex-ante equally safe

and liquid deposits, shadow banks offer depositors an early liquidation op-

tion. Consequently, shadow banks have lower funding costs (regulatory ar-

bitrage), but are exposed to liquidity risk and prefer to hold highly liquid

assets.

In the model, all banks trade in the interbank market (e.g., to construct

diversified portfolios or because they face idiosyncratic liquidity shocks).

Consequently, when the aggregate banking sector grows, interbank trading

increases, the interbank market appears deeper and market liquidity—the

ease to sell an asset close to its fundamental value—increases, see also Han-

son et al. (2015). As the inflow of deposits fosters growth of mortgage loans,

the interbank market for mortgage loans becomes deeper and the expec-

ted liquidation value of selling mortgage loans increases. Since the expected

liquidation value of shadow bank assets increases, their funding liquidity

increases. Shadow banks face less liquidity risk and can exploit their regu-

latory arbitrage with respect to the supply of mortgage loans. As a result,

the shadow banking sector grows relative to the regulated banking sector

because the mortgage loan market grows relative to the corporate loan mar-


110 Chapter 4

ket.

The growing shadow banking sector leaves the economy excessively

vulnerable to financial crises because the shadow banking sector creates too

many uninsured deposits compared to the social optimum. As in Brunner-

meier and Pedersen (2009) and Stein (2012), when intermediaries do not

internalize the costs of fire-sales, unregulated private money creation is typ-

ically sub-optimal. In this chapter, we utilize the general equilibrium struc-

ture of the model to show why banks do not internalize this price effect. A

growing shadow banking sector increases the risk that a significant share of

the banking sector must liquidate its assets which reduces liquidity in the

interbank market. Consequently, shadow banks that create more uninsured

deposits increase the banking system’s reliance on liquidity support by the

central bank. However, the expected costs of liquidity support by the central

bank are not affected by the size of the shadow banking sector. As a result,

the increase in liquidity risk is not fully reflected in the expected liquidation

price of shadow banks’ assets and they issue too many uninsured deposits.4

The results presented in this chapter relate to a growing literature em-

phasizing the risks for financial and economic stability of household debt.

First, an inflow of deposits might harm production when mortgage loan

supply crowds out corporate loan supply as investment in physical capital

is more productive than investment in housing, see Benigno and Fornaro

(2014), Bernanke (2005) and Borio et al. (2016). In the model, the total stock

of houses is fixed.5 Hence, the increase in mortgage lending is collateral-

ized by the increase in the price of the underlying asset rather than by an

increase in the total amount of underlying assets. That is, the economy is

increasingly Ponzi-financed (Minsky, 1986). The increase in mortgage loans

supported solely by an increase in house prices does not improve the eco-

4 Mink (2016) and DeAngelo and Stulz (2015) show that banks having access to a very liquidinterbank market in which systemic risk is insured by a lender of last resort leads to excessiveliquidity creation and high bank leverage.

5 Green et al. (2005) argue that housing supply responds relatively inelastic to increasesin housing demand in the short-run. Saiz (2010) shows that most areas in which housingsupply is regarded as inelastic are constrained by the amount of available land related to thegeography of the area.



nomy’s production capacity and leaves the economy vulnerable to future

house price declines.6 Empirical evidence reported by Mian and Sufi (2014)

and Mian et al. (2016) shows indeed that household debt, predominantly

mortgage loans, is an important determinant of business cycle fluctuations.

Prudential authorities in some countries introduced restrictions on ad-

missible loan-to-value (LTV) ratios to create a precautionary buffer against

house price fluctuations. Here we show two additional potential benefits

from these LTV limits. First, they mitigate house price and thereby mortgage

supply fluctuations when shocks hit the economy. Hence, LTV limits do not

only provide a larger buffer to protect borrowers against house price fluc-

tuations but, also simultaneously attenuate fluctuations in house prices and

mortgage supply. These results are in line with the findings of Wong et al.

(2011) which emphasize the importance of LTV caps in reducing systemic

risk originating from the boom-and-bust cycle of housing markets. Second,

LTV limits reallocate bank lending from mortgage loans to corporate loans,

not only in steady state but also when interest rates fall and credit supply in-

creases. As a result, a larger share of the increase in credit supply is allocated

to firms investing in physical capital which benefits the economy’s produc-

tion capacity. These results emphasize the importance of macroprudential

tools like LTV limits in safeguarding financial and economic stability.

This chapter is also related to a growing literature on financial stability.

Absent a deposit guarantee system, a large shadow banking sector under-

mines financial and economic stability. As described by Diamond and Dyb-

vig (1983), the liquid character of bank liabilities and the illiquid character

of bank assets make these banks intrinsically prone to runs. Brunnermeier

(2009), Brunnermeier and Pedersen (2009) and Brunnermeier and Sannikov

(2014) describe how banks that fund themselves with liquid short-term de-

posits to finance illiquid long-term investments are more vulnerable to li-

quidity risk. Pozsar et al. (2010) and Adrian and Ashcraft (2012) argue that

deposit insurance and a liquidity backstop provided by the central bank are

6 Glaeser et al. (2008) show indeed that places with more elastic housing supply have fewerand shorter house price bubbles.


112 Chapter 4

key to keep consumers calm and their claims liquid. However, by providing

liquidity insurance to banks that is not actuarially fair priced, banks have a

competitive advantage in creating risk free and liquid claims. It is, precisely

this free liquidity insurance that induces shadow banks to issue too many

deposits rather than raising equity, leaving the financial sector vulnerable to

liquidity crises.7

In theory this externality and thereby the consequences for financial sta-

bility could be regulated by means of a Pigouvian tax. In practice, how-

ever, it is hard to determine the optimal level of this tax. Stein (2012) sug-

gests therefore that the regulator should supply tradable permits that allow

banks to create deposits. The market price of these tradable permits helps

to identify the externality. Nevertheless, the optimal amount of permits re-

mains a guess and, if anything, the system increases regulatory arbitrage

between regulated and unregulated banks. Here, we propose a more direct

approach that does not rely on unobservables and affects shadow banks and

regulated banks equally as it works through market prices. The central bank

should provide households access to interest-paying central bank deposits.

In doing so, the opportunity costs for households of holding bank deposits,

as opposed to interest bearing central bank deposits, increases. This means

that banks have to offer a higher interest rate on deposits to persuade house-

holds not to convert their deposits into central bank deposits. If the interest

rate on central bank deposits is sufficiently high, the central bank eliminates

the incentive for both regulated and shadow banks to finance themselves

with deposits rather than equity.

The rest of the chapter is organized as follows. Section 4.2 describes the

correlation presented in Figure 4.4 in more detail. Section 4.3 presents the

model. Section 4.4 presents the simulation results. Section 4.5 discusses the

policy implications and Section 4.6 concludes.

7 In this chapter we use a macro-perspective to motivate the externality. Stein (2012), Green-wood et al. (2015) and Greenwood et al. (2016) motivate a similar externality from the per-spective of an individual bank and also argue that in its presence banks create too manyuninsured deposits.



4.2 Stylized facts extended

In this section we examine more carefully which factors drive the correlation

presented in Figure 4.4. Specifically, we control for real business cycle activ-

ity to ensure that the correlation in Figure 4.4 is not driven by an omitted

variable or underlying trend. Also, Gertler et al. (2016) suggest that finan-

cial innovation (mostly securitization of mortgages) was the main driver of

shadow bank growth which led to more leverage capacity at shadow banks,

a decrease in lending rates and more mortgage lending. First, we control

for financial innovation by including the growth rate of the asset backed

securities and mortgage backed securities markets. Second, we estimate a

vector autoregression in an attempt to control for reverse causality. Finally,

the correlation in Figure 4.4 is biased when the growth rate of mortgage

loans is by definition equal to the growth rate of the shadow bank balance

sheet. Although we will argue that this form of simultaneity is unlikely, we

replace the growth rate of mortgage loans by the growth rate of mortgage

loans supplied by private depository institutions only. This growth rate is

less likely to by determined simultaneously with the growth rate of shadow

bank assets.

4.2.1 Linear regression model

To examine more carefully whether the correlation is caused by any of these

factors, we estimate the following linear regression model for the U.S. bank-

ing sector:

∆ ln (Ybt ) = α0 + α1∆ ln (Mtotal

t ) + α2∆ ln (Ctotalt ) + βBreal

t + γZtotalt + εt

(4.1)

where Ybt denotes either the total amount of regulated (rb) or shadow bank

(sb) financial assets, b ∈ (sb, rb), Mtotalt denotes the total amount of mort-

gage loans and Ctotalt denotes the total amount of corporate loans in the U.S.,

Brealt controls for real business cycle activity (real GDP growth, the Federal

Funds rate and CPI inflation) and Ztotalt controls for financial innovation and


114 Chapter 4

includes both the growth rate of the total asset backed securities (ABS) and

mortgage backed securities (MBS) markets in the U.S., see Tables 4.A.1 and

4.A.2 in Appendix 4.A for details.8

The coefficients in Equation (4.1) are subject to a simultaneity bias when

the growth rate of mortgage loans and the growth rate of corporate loans

determine, to a large extent, the growth rate of the bank balance sheet Ybt .

However, as shadow banks and regulated banks only constitute a relatively

small share of the total U.S. financial sector, this bias is arguably small. These

shares for shadow banks and regulated banks range from 5 and 42 percent in

1954 to 22 and 18 percent in 2017, respectively (see also Figure 4.3). In addi-

tion, mortgage loans account for (on average) 22 percent of the total amount

of financial assets in the U.S while corporate loans account for only 6 percent

of the total amount of financial assets. About half of these mortgage loans

(48 percent) are supplied by private depository institutions, i.e., regulated

banks. To estimate whether a simultaneity bias is driving our results, we

also estimate Equation (4.1) for shadow banks and replace the growth rate

of the total amount of mortgage loans, by the growth rate of mortgage loans

supplied by private depository institutions only.

We estimate Equation (4.1) with Ordinary Least Squares. The results are

presented in Table 4.1. Columns (1) and (2) present the estimation results for

the growth rate of regulated bank assets. All regressors are significant and

have the expected sign. The coefficients on mortgage loan growth (α1) and

corporate loan growth (α2) are not significantly different from each other.

These results suggest that both types of assets are equally important for the

growth rate of regulated banks. The growth rate of the ABS and MBS mar-

kets (γ = 0.089) correlates significantly with the growth rate of regulated

banks. The coefficient is, however, relatively small and suggests that growth

of the ABS and MBS markets is not an important factor for the growth rate

of the regulated banking sector.

The results for shadow banks are presented in columns (3) and (4) of

Table 4.1. Shadow bank growth correlates strongly with the growth rate

8 All variables are stationary at the 5% significance level.



of mortgage loans (α1 = 0.646). Also the growth rate of corporate loans

is significantly correlated with the growth rate of shadow banks. However,

it appears that for shadow banks the growth rate of corporate loans is less

important. The size of the coefficient on corporate loan growth α2 = 0.176,

which is about one-fourth of the size of the coefficient on mortgage loan

growth α1. These results suggest that the growth rate of the mortgage loan

market is much more important for shadow bank growth than the growth

rate of the corporate loan market.

The growth rate of the market for ABS and MBS also significantly cor-

relates with the growth rate of the shadow banking sector. However, the

coefficient γ = 0.068 is again small. These results suggest that shadow bank

growth is not strongly correlated with the expansion of the ABS and MBS

market.

Finally, columns (5) and (6) present the results for shadow banks were

we have replaced the growth rate of mortgage loans by the growth rate of

mortgage loans supplied by private depository institutions only. Although

this variable does not capture the full dynamics of the mortgage loan mar-

ket, the coefficients are no longer subject to a simultaneity bias. The coef-

ficient on mortgage loan growth drops from 0.646 tot 0.378, which is still

significantly larger than the growth rate on corporate loan growth which is

0.175. These results suggest that an increase in the amount of mortgage loans

supplied by private depository institutions also correlates significantly with

the growth rate of shadow bank assets.

4.2.2 Multivariate regression model

For shadow banks, the coefficients in Table 4.1 on the real economic con-

trol variables (β1, β2, β3) are either insignificant or have an unexpected sign.

These coefficients can be biased due to reverse causality when the growth

rate of the shadow banking sector also affects the growth rate of GDP, the

inflation rate and the Federal Funds rate. In an attempt to control for this


116 Chapter 4

Table 4.1. Estimation results Equation (4.1)

Regulated banks Shadow banks Shadow banks

Variables Coefficients Prob. Coefficients Prob. Coefficients Prob.(1) (2) (3) (4) (5) (6)

Growth of mortgages loans (α1) 0.279 0.000 0.646 0.000(0.044) (0.073)

Growth of mortgages loans 0.378 0.000PDI only (α1) (0.065)

Growth corporate loans (α2) 0.215 0.000 0.176 0.000 0.175 0.001(0.026) (0.044) (0.053)

GDP Growth (β1) 0.153 0.000 -0.093 0.180 -0.079 0.302(0.042) (0.070) (0.076)

Federal Funds Rate (β2) -0.328 0.000 0.852 0.000 1.087 0.000(0.072) (0.119) (0.132)

Inflation (CPI) (β3) 0.358 0.000 -0.324 0.018 -0.352 0.018(0.082) (0.135) (0.147)

Growth ABS & MBS assets (γ) 0.089 0.000 0.058 0.035 0.082 0.005(0.016) (0.027) (0.029)

Constant (α0) 2.086 0.000 1.016 0.068 1.934 0.001(0.334) (0.554) (0.576)

Notes: Estimation period 1955Q3 − 2017Q2. Standard errors in parentheses Adjusted R-squared: 0.604 for the growth rate of regulated banks and 0.705 and 0.705 for the growthrate of shadow banks. Abbreviation: Private Depository Institutions (PDI). Source: Author’sown calculations using data from the Flow of funds accounts of the United States and Fed-eral Reserve Bank of St. Louis database.

reverse causality we estimate the following vector autoregression:9

Xt =α0 + Φ(L)Xt−1 + εt, (4.2)

where Φ(L) ≡ Φ0 +Φ1L1 + ...+ΦpLp is a lag polynomial and Xt is a stacked

vector containing the same observed variables as in (4.1). We identify the

VAR by using a Cholesky decomposition. The ordering is as follows: Xt =

[Ybt , Mtotal

t , Ctotalt , Breal

t , Ztotalt ] and we include 4 lags. Results are robust to dif-

ferent lag lengths. Also the ordering of the VAR does not affect the res-

ults. Figure 4.7 in Appendix 4.A shows the results for a different order-

ing: Xt = [Mtotalt , Ctotal

t , Ybt , Breal

t , Ztotalt ], i.e., we allow the growth rate of the

shadow banking sector to affect the growth rate of the mortgage loan mar-

ket and the corporate loan market contemporaneously. Results are very sim-

9 The series do show some signs of co-integration. For this reason we also estimated a VectorError Correction model. The results, which are not presented here, are similar to the impulseresponse functions of the Structural Vector Autoregression.



ilar. The results are also robust to placing the real economic variables Brealt

and/or the growth rate of the ABS and MBS markets Ztotalt first in order.

Figure 4.5 shows the impulse response functions for regulated banks. For

brevity we omitted the impulse response functions for the other variables in-

cluded in Equation (4.2). The graphs shown in the first column show the re-

sponse of mortgage loan growth and corporate loan growth to an unexpec-

ted increase in the growth rate of the regulated banking sector. The growth

rate of both assets increases when the regulated banking sectors grows. The

growth rate of corporate loans responds stronger than the growth rate of

mortgage loans to an increase in the growth rate of regulated banks. The res-

ults suggest that a one percentage point increase in regulated bank growth

is related to a 1 percentage point increase in corporate loan growth, and only

to a 0.5 percentage point increase in mortgage loan growth.

The first graphs in the second and third column show the response of the

growth rate of the regulated banking sector to a shock in the growth rate of

mortgage loans and corporate loans, respectively. Both impulse responses

are insignificant suggesting that the growth rate of regulated banks is not

affected by unexpected increases in the growth rates of these assets. That is,

we cannot find evidence that an increase in the markets for corporate loans

or mortgage loans affects the growth rate of the regulated banking sector.

Figure 4.6 shows similar impulse response functions as in Figure 4.5, but

replaces the growth rate of the regulated banking sector with the growth

rate of the shadow banking sector. It turns out that the results for shadow

banks are different than those for regulated banks. Shadow bank growth

appears to respond positively to a shock in the mortgage growth rate (first

graph in the second column). In contrast, shadow bank growth is unaffected

by an increase in the growth rate of corporate loans (first graph in the third

column). Furthermore, an increase in the growth rate of shadow banks has

no effect on the growth rate of either mortgage loans or corporate loans.

Figure 4.7 shows similar impulse response functions as in Figure 4.6, but

replaces the growth rate of mortgage loans with the growth rate of mortgage

loans supplied by private depository institutions. Results are very similar to


118 Chapter 4

Figure 4.5. VAR estimation results of Equation (4.2) for regulated banks

Corporate loan to regulated bank Corporate loan to mortgage loan Corporate loan to corporate loan

Note: time (year) on the horizontal axis, percentage point devations on the vertical axis.

Regulated bank to Regulated bank Regulated bank to mortgage loan Regulated bank to corporate loans

Mortgage loan to regulated bank Mortgage loan to mortgage loan Mortgage loan to corporate loan

-1

0

1

2

1 2 3 4 5 6 7 8 9 10-1

0

1

2

1 2 3 4 5 6 7 8 9 10-1

0

1

2

1 2 3 4 5 6 7 8 9 10

-1.0

-0.5

0.0

0.5

1.0

1 2 3 4 5 6 7 8 9 10

-1.0

-0.5

0.0

0.5

1.0

1 2 3 4 5 6 7 8 9 10

-1.0

-0.5

0.0

0.5

1.0

1 2 3 4 5 6 7 8 9 10

-2

-1

0

1

2

3

1 2 3 4 5 6 7 8 9 10

-2

-1

0

1

2

3

1 2 3 4 5 6 7 8 9 10-2

-1

0

1

2

3

1 2 3 4 5 6 7 8 9 10

Notes: estimation period 1955Q3–2017Q2, time (quarters) horizontal axis, percentage pointdeviation on the vertical axis. The titles explain the response of one of the variables includedto a shock of any of the variables included. Dotted red lines denote confidence intervals at95% significance level.

the results presented in Figure 4.6: a shock to the growth rate of mortgage

loans affects the growth rate of the shadow banking sector, whereas an in-

crease in the shadow bank growth rate does not affect the growth rate of

mortgage loans. Moreover, replacing the the growth rate of mortgage loans

with the growth rate of mortgage loans supplied by private depository in-

stitutions in reduced the size of the coefficient significantly in Table 4.1. In

contrast, the results in 4.7 are not affected by this change and appear robust.

Evidently these results are not conclusive. They do suggest, however,

that mortgage growth appears to affect shadow bank growth, while we can-

not find strong evidence that shadow bank growth is driving the growth

rate of the mortgage loan market. In the next section we present a model

that is able to explain this apparent causality in more detail.



Figure 4.6. VAR estimation results of Equation (4.2) for shadow banks

Corporate loan to shadow bank Corporate loan to mortgage loan Corporate loan to corporate loan


Shadow bank to shadow bank Shadow bank to mortgage loan Shadow bank to corporate loans

Mortgage loan to shadow bank Mortgage loan to mortgage loan Mortgage loan to corporate loan

-0.5

0.0

0.5

1.0

1 2 3 4 5 6 7 8 9 10

-0.5

0.0

0.5

1.0

1 2 3 4 5 6 7 8 9 10

-0.5

0.0

0.5

1.0

1 2 3 4 5 6 7 8 9 10

-2

-1

0

1

2

3

1 2 3 4 5 6 7 8 9 10-2

-1

0

1

2

3

1 2 3 4 5 6 7 8 9 10

-2

-1

0

1

2

3

1 2 3 4 5 6 7 8 9 10

-2

-1

0

1

2

3

1 2 3 4 5 6 7 8 9 10

Response of GROWTH_SB to GROWTH_SB

Response to Cholesky One S.D. Innovations ± 2 S.E.

-2

-1

0

1

2

3

1 2 3 4 5 6 7 8 9 10

Response of GROWTH_SB to GROWTH_M

Response to Cholesky One S.D. Innovations ± 2 S.E.

-2

-1

0

1

2

3

1 2 3 4 5 6 7 8 9 10


Figure 4.7. VAR estimation results of Equation (4.2) for shadow banks andPDI mortgage loan growth

Corporate loan to shadow bank Corporate loan to mortgage loan Corporate loan to corporate loan


Shadow bank to shadow bank Shadow bank to mortgage loan Shadow bank to corporate loans

Mortgage loan to shadow bank Mortgage loan to mortgage loan Mortgage loan to corporate loan

-1

0

1

2

3

2 4 6 8 10

-1

0

1

2

3

2 4 6 8 10

-1

0

1

2

3

2 4 6 8 10

-2

-1

0

1

2

2 4 6 8 10

-2

-1

0

1

2

2 4 6 8 10

-2

-1

0

1

2

2 4 6 8 10

-2

0

2

4

2 4 6 8 10

-2

0

2

4

2 4 6 8 10-2

0

2

4

1 2 3 4 5 6 7 8 9 10



120 Chapter 4

4.3 The model

The model embeds elements of the financial structure developed in Stein

(2012), Gennaioli et al. (2013) and Hanson et al. (2015) in a general equi-

librium context. Specifically, regulated banks are regulated while shadow

banks are not. Since households value deposits for their safety and liquidity,

the deposit rate trades at a discount vis-a-vis the rate on bank equity. Con-

sequently, absent regulation, both shadow banks and regulated banks prefer

to finance their lending with deposits rather than equity as the latter is more

expensive. Both banking types can fund mortgages and corporate loans. In

this chapter, corporate loans are used by firms to buy physical capital and

mortgage loans are used by impatient households to fund a house.

Aggregate productivity risk is introduced to create scope for deposit in-

surance and liquidity risk. Aggregate risk cannot be diversified and poses a

potential threat to the risk-free claim of depositors. The central bank requires

regulated banks to insure all downside aggregate risk in the deposit guar-

antee scheme (DGS). Shadow banks are unregulated and offer households

an early liquidation option to create risk-free claims (Stein 2012 and Hanson

et al. 2015). For shadow banks the early liquidation option is less costly, but

offering this option creates additional liquidity risk. Unregulated shadow

banks cannot borrow directly from the central bank. Consequently, if a pess-

imistic signal about the future state of the world occurs, shadow banks must

sell their assets in the interbank market to regulated banks in order to remu-

nerate their depositors. The expected liquidation value of shadow bank as-

sets is key and determines the shadow banks’ comparative advantage vis-a-

vis regulated banks. If the expected liquidation value is low, shadow banks

have no comparative advantage and only regulated banks exist. If the expec-

ted liquidation value is high, shadow banks have a comparative advantage

and can exploit any regulatory arbitrage.

The model describes three sources of heterogeneity: patient (p) and im-

patient (i) consumers denoted by the superscript j ∈ p, i, regulated banks

(rb) and shadow banks (sb) denoted by the superscript b ∈ rb, sb, and



mortgages ( f ) and corporate loans (e) denoted by the superscript ι ∈ f , e.Impatient consumers discount the future more heavily than patient con-

sumers. As a consequence, the latter will prefer to save while impatient

consumers will prefer to borrow. Both households may hold central bank

money (henceforth: cash) which does not pay interest or buy risk-free money-

like claims (henceforth: deposits) from risk neutral banks because both are

necessary to consume. Thus, indirectly, consumption is subject to a cash-in-

advance constraint. Patient households might also buy equity of both bank-

ing types in order to save part of their income.

4.3.1 Aggregate risk

The return on bank assets (corporate loans and mortgages) πs depends on

the state of the world s ∈ S. At time t all banks assume that state s ∈ S

materializes with probability $s > 0 where ∑s $s = 1. For reasons of tract-

ability, we assume that at each point in time banks expect only 3 different

states: S = g, b, d referring to a good, bad and disaster state, respectively.

Accordingly, πg(·) > πb(·) > πd(·) denote the return on bank assets in the

respective states. Between time t and t + 1 we assume that some informa-

tion about the future economic state can be observed S′= H, L, which can

be either optimistic (H) or pessimistic (L).The probability tree in Figure 4.8

formalizes the discussion where P(u) denotes the probability of an up node

and P(d) denotes the probability of a down node. If an optimistic signal is

observed, agents know with certainty that the disaster state will not occur.

If a pessimistic signal is observed, all three states can occur.10

The following notation is introduced for brevity purposes:

Et(πs) ≡ P(u)Et|S′=H(πs) + P(d)Et|S′=L(πs) = 1, (4.3)

Et|S′=H(πs) ≡ P(u|H)πg + P(d|H)πb, (4.4)

10 These assumptions can easily be generalized. In particular, S could include a continuousset of states s and a continuous set of signals might be observed that are consistent withthe results presented below. Crucial, however, is that a set of signals can be observed withprobabilities of a disaster states that are negligibly small (or absent) to keep depositors calmwhile pessimistic signals result in depositors withdrawing their shadow bank deposits.


122 Chapter 4

Figure 4.8. Probability tree for the occurrence of a signal and the states of theworld.

t

L

d : πdt + 1

P(d|L)

b : πb1− P(u|L)− P(d|L)

g : πg

P(u|L)

P(d)

H

P(d|H)

P(u|H)

P(u)

Notes: P(u) denotes the probability for an up node and P(d) denotes the probability of adown node. After the signal, the probabilities of an up node or down node are conditionalon an optimistic (H) or pessimistic (L) signal. πg(·) > πb(·) > πd(·) denote the productivityin the good, bad and disaster state, respectively.

Et|S′=L(πs) ≡ P(u|L)πg + (1− P(u|L)− P(d|L))πb + P(d|L)πd, (4.5)

where Et(πs) is the expected return at time t before the signal occurs which

we normalize to unity and Et|S′=H(πs) and Et|S′=L(πs) denote the expected

return associated with an optimistic or a pessimistic signal, respectively.

4.3.2 Real economy: households and firms

The economy consists of two types of infinitely lived households, the only

difference being that the impatient household has a lower discount factor

than the patient household βi < βp. Consequently, in equilibrium patient



households save, while impatient households borrow. The economy occu-

pies a continuum of households with their mass normalized to unity. House-

holds derive utility from consumption Cjt , holding deposits or cash Mj

t, leis-

ure (1− Ljt) and owning a house H j

t .11 The corresponding household utility

function takes the following functional form:

U jt = Et

∞

∑t=0

(βj)t

[(Cj

t)η(H j

t)1−η]1−σc

1− σc +γm(Mj

t)1−σm

1− σm −γ

jl(Lj

t)1+σl

1 + σl

,

(4.6)

where deposits Mjt can be supplied by regulated banks Mj,rb

t and shadow

banks Mj,sbt or by the central bank Mj,cb

t in the form of cash, Et is the expect-

ation operator, 1− η denotes the weight of housing, σc, σm and σl denote,

respectively, the inverse of the elasticities with respect to consumption, de-

posits and work-effort, γm and γjl denote the weights of deposits and labor

relative to consumption in the utility function.

Residential houses play a key role in the model. In Equation (4.6) we as-

sume that households consume a consumption bundle that contains regular

consumption goods and their stock of houses. Consequently, if consumption

increases, housing demand increases because consumers equate the mar-

ginal rate of substitution to the price differential between house prices (qht )

and consumer prices (in this model normalized to unity). However, as res-

idential houses do not perish each period like consumption goods, owning

a house also yields a potential capital gain rht ≡ qh

t /qht−1 − 1. Accordingly,

both a decrease in the lending rate or an expected increase in house prices

increase housing demand.

If households receive a pessimistic signal, they liquidate their deposits

in the shadow banks and convert it in regulated bank deposits or cash. If the

11 Deposits in the utility function can be motivated by a cash-in-advance constraint as house-holds need deposits to pay for consumption. While deposits can be used directly for pay-ment, equity must first be converted into a liquid asset like deposits before a household canuse it for payment. This liquidity difference motivates why, apart from safety reasons, bothtypes of households value deposit holdings over equity when interest rates on both assetsare the same.


124 Chapter 4

signal is optimistic, households remain calm and hold on to their deposits in

the shadow banks. The option to liquidate at the intermediate stage makes

the shadow bank deposits ex-ante perfectly safe and liquid. Regulated bank

deposits are fully protected by the deposit guarantee system (DGS). Hence,

in the steady state households do not hold cash because the central bank

does not pay interest and cash is therefore inferior to deposits. Cash becomes

attractive, however, when deposit interest rates fall sufficiently (below zero)

or when the regulated banking sector is no longer able to create perfectly

safe and liquid claims.

Households maximize their utility subject to their budget constraints.

The patient household’s budget constraint is represented by:

Mpt + Qt + qh

t (Hpt − Hp

t−1) = (1 + imt−1)Mp

t−1 − imt−1Mp,cb

t−1+

(1 + iqt−1)Qt−1 + rh

t Hpt−1 − Cp

t + WtLpt + θ(Πb

t + Πpt ) (4.7)

where Qt = Qrbt + Qsb

t denotes the equity stakes of the patient households in

the regulated and shadow banks respectively, imt , either im,rb

t or im,sbt , denote

the rates on regulated and shadow bank deposits respectively, and iqt , either

iq,rbt or iq,sb

t , denotes the risky interest rates on regulated and shadow banking

equity respectively.12 The term Wt denotes the wage rate patient households

receive for supplying labor to the firms and Πpt and Πb

t denote firm profits

and bank profits redistributed to households where θ denotes the share of

patient households in the economy.13 Finally, households own a housing

stock H jt and realize a return on the house defined by rh

t . We assume that

a house is perfectly divisible. Each period, households can therefore buy or

sell part of their house in line with their demand for housing for a price qht .

The impatient households have the same utility function as the patient

households. They own, however, potentially different assets because they

are the savers and therefore also the investors in the economy. Particularly,

impatient households have two investment opportunities for which they

12 Note that imt−1 Mp,cb

t−1 in (4.7) accounts for the fact that cash does not pay interest.13 As the economy is fully flexible, firms profits are always zero, while bank profits flow tothe bank equity holders.



can borrow: they can invest in physical capital Kt or in housing Ht. Physical

capital has a cost ret and yields a return rk

t while housing costs r ft and yields

a return rht . The impatient household’s budget constraint is represented by:

B ft + Be

t −Mit =qh

t (Hit − Hi

t−1) + (1 + i ft−1)B f

t−1 + (1 + iet−1)Be

t−1−

(1 + imt−1)Mi

t−1 + imt−1Mi,cb

t−1 − rht Hi

t−1 −WtLit − rk

t Kt−1−

(1− θ)(Πbt + Πp

t ) + Cit + It, (4.8)

where B ft denotes mortgages for the nominal value of the house qh

t Hit and Be

t

denotes corporate loans for the nominal value of physical capital qkt Kt−1, i f

t

denotes the gross lending rate for mortgages and iet denotes the gross lend-

ing rate for physical capital. Impatient households rent out their physical

capital stock to firms for a rental rate rkt . The physical capital stock accumu-

lates according to:

Kt+1 = Kt(1− δ) + It

(1− φ

2

(It

It−1− 1)2 )

, (4.9)

where It denotes net investment in the physical capital stock and δ denotes

the deprecation of the physical capital stock. The second term in round

brackets in (4.9) denotes physical capital adjustment costs. The parameter

φ which denotes the degree of adjustment costs, determines to some degree

shifts in demand between physical capital and housing as it determines the

elasticity of physical capital supply.

The loan (Bιt) cannot be larger than the real value of its collateral. Without

this constraint, impatient consumers would like to borrow indefinitely to

finance housing, physical capital, but also consumption. As the main pur-

pose is to distinguish between investment in two types of assets, we restrict

borrowing for consumption. For this reason, the following inequality con-

straints are postulated for impatient households, Appendix 4.B presents a

proof that (4.10) and (4.11) hold with equality:

qht Hi

t ≥ ζ f B ft , (4.10)


126 Chapter 4

qkt Kt−1 ≥ ζeB

e

t , (4.11)

where ζ f is a cap on admissible loan-to-value ratios for mortgage loans and

ζe is a cap on admissible loan-to-value ratios for corporate loans. Inequalities

(4.10) and (4.11) state that the amount borrowed for housing B ft and physical

capital Be

t cannot be larger than the value of the underlying asset that serves

as collateral qht Hi

t and qkt Kt−1 corrected for the loan-to-value limit.

Household preferences determine both the return on banking equity and

the deposit rate. Intermediation adds value as households are willing to pay

a premium for a safe and liquid asset that pays interest. Alternatively, house-

holds can hold cash supplied by the central bank, which is safe but does not

pay interest. Hence, as long as banks create completely safe deposits and

offer a positive return on deposits, households are willing to hold deposits

rather than cash. Banks have access to deposit insurance and the interbank

market to insure liquidity risk while households have no access to these in-

stitutions and as such cannot construct a diversified portfolio to eliminate

credit and liquidity risk. For this reason, households do not want to invest

their endowment directly in corporate loans or mortgages.

The option for households to convert deposits into cash is a source of ag-

gregate liquidity risk in the banking sector. Households only convert their

deposits into cash when regulated banks are no longer able to guarantee the

safety and liquidity of their deposits. This might happen when the interbank

market stops functioning properly, for example, because shadow banks trig-

ger a loss spiral. Regulated banks use the interbank market to diversify their

portfolio and insure idiosyncratic liquidity risk. Without interbank market

regulated banks loose their ability to create safe and liquid deposits and

the DGS buffers are not large enough to cover the increase in liquidity risk.

Consequently, households are more likely to convert their deposits into cash

which does not pay interest, but is completely safe and liquid. It is precisely

this mechanism we will use later on to motivate the increase in aggregate

liquidity risk when the shadow banking sector grows.

Patient households maximize (4.6) subject to (4.7) with respect to con-



sumption, deposits, labor supply, housing accommodation and bank equity.

Impatient households maximize (4.6) subject to (4.8), (4.9), (4.10) and (4.11)

by choosing consumption, housing accommodation, deposits, labor sup-

ply, mortgages, corporate loans, physical capital and investment, see Ap-

pendix 4.B for details. Consequently, and in contrast to Stein (2012), Gen-

naioli et al. (2013) and Hanson et al. (2015), depository funding, equity fund-

ing and household borrowing demand are all endogenously determined in

the model. Additionally, we model an explicit outside option that enables

households during financial stress to withdraw liquidity from the system

by increasing their holdings of cash.

Firms rent their physical capital from the impatient households and hire

labor from both types of households to minimize their production costs sub-

ject to the aggregate production technology:

Yt = At(Kt−1)1−α(Lt)

α, (4.12)

where Yt denotes production, Lt = Lpt + Li

t is the sum of patient and im-

patient household labor, At denotes an aggregate productivity index which

follows a stochastic process At = exp(ηat ), where ηa

t = ρaηat−1 + εa

t and εat is

an i.i.d. productivity shock ∼ (0, σa).

4.3.3 Regulated and shadow banks

In the model two types of banks exist: regulated banks that are regulated

and shadow banks that are unregulated. Regulated regulated banks are ob-

liged to insure their deposits in the DGS and have access to the central bank

lending facility. Regulated banks pay an actuarially fair price for this deposit

insurance that pays-off in the disaster state (Hanson et al., 2015). House-

holds can convert their regulated bank deposits into cash because regulated

banks can borrow from the central bank. Shadow banks do not particip-

ate in the deposit insurance scheme and cannot borrow from the central

bank. Consequently, shadow bank deposits cannot be converted into cash,

but only into regulated bank deposits. Therefore, if between t and t + 1 a


128 Chapter 4

pessimistic signal about the future state of the world occurs, depositors li-

quidate their shadow bank deposits which are no longer risk-free. To repay

their depositors, the shadow banks must liquidate their assets in the interb-

ank market. The expected liquidation value determines how much safe and

liquid deposits a shadow bank can issue ex-ante and thereby determines

indirectly the shadow banks’ funding cost.

In the main text, only fully diversified portfolios without idiosyncratic

risk are considered. Appendix 4.E shows that both regulated banks and

shadow banks will always completely diversify their portfolio if diversifica-

tion costs are reasonably low. For example, when the interbank market func-

tions properly transaction costs are low and banks can easily trade assets to

have diversified portfolios. We therefore assume that a properly functioning

interbank market is a necessary condition for the banking sector to construct

a fully diversified portfolio. Without a properly functioning interbank mar-

ket, bank deposits are no longer perfectly safe and liquid, and households

might convert deposits into cash.

Regulated and shadow banks, denoted by the superscript b ∈ (sb, rb), re-

spectively, have the same objective function except for the deposit insurance

premium. Each period the banks issue Mbt units of deposits and Qb

t units of

equity and promise to repay (1+ im,bt )Mb

t and (1+ iq,bt )Qb

t in the next period.

These funds are used to lend mortgages B f ,bt and corporate loans Be,b

t . The

objective function for both banks can be described by:

Πbt = ie

t Be,bt + i f

t B f ,bt − im,b

t (Mbt + Mb,x

t )− iq,bt Qb

t − Ξb − ξDt, (4.13)

where i ft and ie

t are the expected returns on investment in mortgages and

corporate loans respectively, Mbt is the sum of patient Mp,b

t and impatient

household deposits Mi,bt , and Mb,x

t denote foreign deposits for which de-

mand is specified below. All off-steady state excess returns Πrbt and Πsb

t ac-

cumulate to the equity holders. The term Ξb denotes fixed costs and ensures

that excess returns are zero in equilibrium. Both the deposit rate and equity

rate are in equilibrium pinned down by household preferences while loan



supply is restricted by the collateral constraints. Accordingly, lending rates

might differ from the banks’ weighted average costs of funding which yields

non-zero bank profits without the fixed costs term. The last term is the de-

posit guarantee premium Dt. For regulated banks ξ = 1 and for shadow

banks ξ = 0. The ex-ante actuarially fairly priced deposit guarantee pay-

ment is expressed as:

Dt = χ[(1 + i f

t )B f ,rbt + (1 + ie

t)Be,rbt

], (4.14)

where χ = P(d)P(d|L)(πb − πd) denotes the DGS cost per unit of invest-

ment in the risky assets. The deposit insurance needs to cover only the dif-

ference between the bad and disaster state as regulated banks holds suffi-

cient equity to remain solvent in the good and bad state. Both types of banks

satisfy the same budget constraint:

Be,bt + B f ,b

t + ξ (Dt + Rt) ≤ Qbt + Mb

t + Mb,xt , (4.15)

where Rt denotes deposits, or reserves, at the central bank. Only regulated

banks have access to central bank deposits. By assumption central bank

deposits do not pay interest and are completely safe. Moreover, regulated

banks are not required to hold these central bank deposits which ensures

that in equilibrium they will not lend from the central bank to hold central

bank deposits.

The market also requires banks to hold sufficient equity. The equity buf-

fer constraint states that in the worst possible state banks should be able to

repay their risk-free deposits. Since both types of banks adopt a different

business model with respect to the creation of risk free claims, the regulated

bank equity buffer constraint is different from the shadow bank equity buf-

fer constraint. The regulated bank equity buffer constraint (or risk-weighted

assets constraint) is specified by:

Rrbt + πb

[(1 + i f

t )B f ,rbt + (1 + ie

t)Be,rbt

]≥ (1 + im,rb

t )(Mrbt + Mrb,x

t ).

(4.16)


130 Chapter 4

The buffer constraint states that regulated banks should have sufficient equity

to ensure that the return in the bad state of the world is sufficient to cover all

risk-free deposits. Deposit insurance guarantees the repayment of deposits

in the disaster state and is therefore not of interest to the market.

The shadow bank equity buffer constraint is specified by:

Rsbt + κ

ft (1 + i f

t )B f ,sbt + κe

t (1 + iet)Be,sb

t ≥ (1 + im,sbt )(Msb

t + Msb,xt ),

(4.17)

where 0 < κft , κe

t < 1 specify the percentage of value that is retrieved when

the shadow banks liquidate their assets in the interbank market. It is pos-

sible to read the participation constraint as a “worst case scenario outcome”

which, for the shadow bank, is the realization of a pessimistic signal. In that

case, households liquidate their deposits and shadow bank must sell their

assets in the interbank market to remunerate the households.

In Appendix 4.C we show that for both banks the budget and equity

buffer constraints hold with equality. Hence, it is possible to substitute the

constraints (4.15) and (4.16) in (4.13) to obtain the regulated bank maxim-

ization problem. Likewise, substituting the constraints (4.15) and (4.17) in

(4.13) gives the shadow bank maximization problem. From these maximiz-

ation problems we can induce that as long as the return on a loan is larger

than the costs of funding and insurance, both banks will maximize asset

holdings and minimize the amount of equity funding.

4.3.4 How do banks invest?

Regulated banks pay for deposit insurance costs summarized by the para-

meter χ which is assumed to be a fixed percentage of the total asset return.

Shadow banks circumvent the deposit insurance costs but are limited in

their creation of deposits by the expected liquidation value κιt. Equating the

weighted average costs of funding of regulated banks and shadow banks,

see Appendix 4.D, we can distinguish three different scenarios depending

on the relative weighted average costs of funding of regulated banks versus



shadow banks. Proposition 4.1 summarizes the three scenarios:

Proposition 4.1.

a) If κet <

πb1+χie

tand κ

ft < πb

1+χi ft, liquidity in the interbank market for both corporate

loans and mortgages is too low for shadow banks to be able to compete with regulated

banks. Regulated banks specialize in both mortgages and corporate loans.

b) If κet < πb

1+χiet

and πb

1+χi ft< κ

ft , the interbank market for mortgages is suffi-

ciently liquid for shadow banks to overcome the expected liquidation cost disadvant-

age. Regulated banks specialize in corporate loans while shadow banks specialize in

mortgages.

c) If κet > πb

1+χiet

and πb

1+χi ft> κ

ft , the interbank market for corporate loans is suf-

ficiently liquid for shadow banks to overcome the expected liquidation cost disad-

vantage. Regulated banks specialize in mortgages while shadow banks specialize in

corporate loans.

Proof in Appendix 4.D. It is, of course, possible that shadow banks have a

competitive advantage in supplying both mortgage loans and corporate loans.

However, it is not possible for shadow banks to exist without regulated

banks because the viability of the shadow bank business model depends

on the existence of regulated banks that buy shadow bank assets in case of

a liquidation. If shadow banks have lower costs in supplying both corpor-

ate loans and mortgages they specialize in the assets in which they have a

comparative advantage which brings us back to either Proposition 4.1-b or

c.

4.3.5 Expected liquidation value

Whether regulated banks or shadow banks have lower funding costs de-

pends on the liquidation value κιt. We assume that the fundamental liquid-

ation values are affected by the relative depth of the interbank market for

mortgages or corporate loans and by aggregate liquidity risk which depends

on the relative share of deposits that are uninsured, see Stein (2012) and


132 Chapter 4

Hanson et al. (2015) for a similar approach. Accordingly, the liquidation val-

ues per unit of investment are specified by:

κιt = (1−ω)

(Et|S′=L(πs)

)ϕι

1

(Bι

tBt

)ϕι

2

(Msb

tMt

), (4.18)

where ω = P(d|L)(πb − πd) denotes the deposit insurance costs regulated

banks must pay when they buy shadow bank assets, Et|S′=L(πs) denotes the

fundamental price of the loan when a pessimistic signal occurs and ϕι (·)is a function that specifies the impact of a deeper interbank market for cor-

porate loans and mortgages (Bιt) relative to the entire market (Bt) and more

uninsured deposit creation (Msbt ) relative to total bank deposits (Mt) on the

liquidation value.

The intuition behind (4.18) is as follows. When regulated banks buy

shadow bank loans, regulated banks must insure these loans in the deposit

guarantee system. The term (1−ω) incorporates the insurance costs which

only consist of the probability that a bad state of the world will occur con-

ditional on the occurrence of a pessimistic signal. In Appendix 4.E we show

that when shadow banks diversify their asset portfolio, the liquidation costs

decrease because idiosyncratic risk no longer needs to be insured. This provides

an incentive for shadow banks to diversify their portfolio. In particular, if

the diversification costs are sufficiently low, shadow banks will always com-

pletely diversify their portfolio because a diversified portfolio has a higher

liquidation value.

In case a pessimistic signal about the future state of the world occurs

(S′= L), the expected returns fall from Et(πs)iι

t+1 = 1 to Et|S′=L(πs)iιt+1

< 1. The loan contracts, however, are predetermined at the beginning of

period t under a condition of zero bank profits and therefore the lending

rate equals the banks’ funding costs (the net present value of a loan is zero).

Consequently, the net present value of a bank loan becomes negative when

a pessimistic signal occurs. The reverse holds when a signal about the fu-

ture state of the world is positive. Regulated banks will therefore only buy

shadow bank loans if the price of these loans falls sufficiently to compensate



for the loss in value. The fundamental liquidation value after a pessimistic

signal occurs therefore yields Et|S′=L(πs)/Et(πs) < 1 where Et(πs) = 1.

The function ϕι (·) consists of two terms that create a wedge between the

fundamental liquidation value and the value in the interbank market. First,

the depth of the interbank market positively affects the expected liquidation

value as a deeper interbank market makes it easier to find a counterparty,

∂ϕι(·)/∂Bιt > 0. We assume that the relative ease to find a counterparty de-

pends on the size of the market for asset ι (Bιt) relative to the total size of

the market (Bt). Motivated by the fact that individual banks trade in the in-

terbank market, e.g., to construct diversified portfolios or because they face

idiosyncratic liquidity shocks, a larger banking sector in terms of assets res-

ults in more interbank trading. In the limit, when the depth of the market

goes to infinity, no liquidation discount is added and the expected liquida-

tion price of the asset equals its fundamental value: lim(Bιt/Bt)→0ϕι(·) = 1.

Without an interbank market for the asset, the asset can never be sold to

another party and the liquidation price equals zero: lim(Bιt/Bt)→1ϕι(·) = 0.

Second, the creation of shadow bank deposits decreases the expected li-

quidation value, ∂ϕι(·)/∂Msbt < 0. In case a pessimistic signal occurs, more

shadow bank deposits are withdrawn and more shadow bank assets are

sold. Regulated banks buy shadow bank assets, but face aggregate liquidity

risk as households might convert some of their deposits into cash. We as-

sume that the ability of regulated banks to guarantee the safety and liquidity

of their deposits depends on liquidity in the interbank market. The expected

market liquidity therefore depends on the amount of shadow bank deposits

(Msbt ) relative to the total amount of deposits (Mt). In the limit, when all de-

posits are created by shadow banks, the expected liquidation value goes to

zero because all shadow banks sell in case a pessimistic signal occurs and no

regulated bank exists that buys, lim(Msbt /Mt)→∞ϕι(·) = 0. The interbank

market ceases to exist. Without shadow banks, no liquidation discount is

added because no bank ever liquidizes its assets, lim(Msbt /Mt)→0ϕι(·) = 1.

Brunnermeier and Pedersen (2009), Stein (2012) and others showed that

the creation of uninsured deposits is associated with a negative externality.


134 Chapter 4

Banks do not take into account that selling an asset affects the price of the

asset which leads to further losses. Consequently, the initial decrease in the

liquidation value is amplified and the ex-ante expected liquidation value

differs from the ex-post realized liquidation value. In this chapter we take

the negative correlation between more shadow bank deposits and the ex-

pected liquidation value as given ∂κι/∂Msbt < 0. Instead, we analyze why

this negative externality is not priced by the market.

4.3.6 Externalities

At the aggregate level the depth of the interbank market and the amount of

shadow bank deposits affect the expected liquidation value of shadow bank

assets. If, however, shadow banks take the expected liquidation discount as

given and do not include the incremental impact they have on its value,

two externalities emerge. In this case, shadow banks maximize their profits

(4.13) subject to the budget (4.15) and bank equity constraints (4.17). The

FOCs w.r.t. loans and deposits yield:

iιt = iq,sb

t − µsbt κι

t(1 + iιt), (4.19)

im,sbt = iq,sb

t − µsbt (1 + im,sb

t ), (4.20)

where µsbt denotes the shadow value of the bank equity buffer constraint.

We use that the shadow value of the budget constraint equals the costs of

bank equity, see Appendix 4.C. In contrast, maximizing shadow bank profits

w.r.t. loans and deposits taking into account the incremental impact shadow

banks have on the liquidation parameter yields:

iιt =iq,sb

t − µsbt (1 + iι

t)

[kι

t +∂kι

t∂Bι

tBι

t

], (4.21)

im,sbt =iq,sb

t − µsbt

((1 + im,sb

t )−∑ι

∂kι

t∂Ms

t(1 + iι

t)Bιt

). (4.22)

The impact of ignoring the incremental impact of shadow banks on the li-

quidation parameter is twofold. First, an increase in credit supply for mort-



gages or corporate loans by shadow banks increases the depth of the market

for mortgages and corporate loans. Consequently, the shadow bank equity

buffer constraint relaxes because µsbt (1 + iι

t)∂κιt/∂Bι

t > 0. Hence, if shadow

banks neglect the incremental impact they have on the depth of the interb-

ank market, they underestimate their marginal costs. Consequently, lending

rates are higher and credit supply and shadow bank leverage are lower than

their social optimal levels.

Second, from a funding perspective, if shadow banks issue deposits,

market liquidity decrease. The shadow bank equity buffer constraint always

binds and accordingly shadow bank deposit creation is at its maximum at-

tainable level. If a shadow bank changes its capital structure by financing

a larger share of its assets with deposits, it realizes a private benefit in the

form of lower financing costs. However, the shadow bank also decreases the

expected liquidation value of other shadow banks represented by a decrease

in κιt because more shadow banks assets are sold when a pessimistic signal

occurs, ∂κιt/∂Ms

t < 0. The equity buffer constraint of all other shadow banks

tightens. Consequently, the deposit rate, shadow bank deposit creation and

shadow bank leverage are above their socially optimal level. The following

proposition summarizes the discussion:

Proposition 4.2.

Let B∗ and M∗ denote the social optimal amounts of shadow bank loans and deposits

and let B′

and M′

denote the optimal amount of shadow banks loans and deposits

from the perspective of the shadow banks. Shadow banks supply too much credit,

B∗ < B′, and create too many deposits, M∗ < M

′, if |∂κι

t/∂Bιt| < |∂κι

t/∂Mst |.

4.3.7 Closure

The real side of the model is closed by imposing the goods market equilib-

rium. Total production is equal to consumption, investment and lump-sum

central bank consumption (which is equal to the deposit premium paid by


136 Chapter 4

regulated banks if not paid out):

Yt = Cpt + Ci

t + It + Dt. (4.23)

We assume foreign deposit demand takes the same functional form as

the domestic deposit demand equation for σm = −1. All endogenous vari-

ables affecting deposit demand (the foreign deposit, lending and bank equity

rate, consumption and housing), except for the domestic deposit rate, are

lumped in a fixed term ϑ. The domestic interest rate provides feedback as an

increase in foreign deposit demand reduces the domestic interest rate which

attenuates the increase in foreign deposit demand. The functional form is

represented by:

Mrb,xt = (εm

t − 1)ϑ log(1 + im,it ), (4.24)

where εmt denotes a foreign deposit demand shock, i.e., a savings glut if

εmt > 1, εm

t = exp(ηmt ), where ηm

t = ρmηmt−1 + εm

t and εmt is an i.i.d. error term

∼ (0, σm).

Housing supply is fixed at an arbitrarily level H:

Hst = H. (4.25)

Prices are perfectly flexible and accordingly there is no role for conven-

tional monetary policy to attenuate macroeconomic fluctuations by setting

the policy rate. However, as Goodhart (1988) argues, the original motivation

for creating most central banks was not maintaining price stability but, as in

this chapter, to provide financial stability. Here the central bank regulates

the banks and fulfills the lender of last resort function when the banking

sector has insufficient funding. Aggregate liquidity can only fall when ag-

gregate demand for cash Mcbt increases. In this case, the banking sector faces

a funding shortfall and needs to borrow from the central bank. Bank bor-

rowing from the central bank is denoted by Bcbt . The central bank balance



sheet is represented by:

Bxt + Bcb

t = Rt + Mcbt . (4.26)

In normal times both non-interest paying deposits at the central bank Rt and

household holdings of cash Mcbt are zero such that borrowing from the cent-

ral bank by banks, Bcbt , is also zero. Moreover, Bx

t denotes borrowing from

the central bank by non-domestic banks (denoted in the domestic currency).

Borrowing by foreign banks is zero in equilibrium and increases when the

aggregate foreign banking sector has insufficient funding.

The intuition behind the transmission of the shock εmt is as follows. For-

eign households withdraw their deposits at foreign banks and deposit these

deposits at domestic banks. Foreign demand for domestic deposits, Mrb,xt ,

increases. As foreign banks have a funding shortfall, they can either bor-

row from domestic banks or the central bank. We assume that the interbank

market does not provide funding for these foreign funding shortfalls. For-

eign banks therefore lend from the central bank, while domestic banks de-

posit their excess funds at the central bank. Both Bxt and Rt increase. Central

bank deposits do not pay any interest, while bank deposits do pay interest.

Therefore the domestic banking sector decreases the deposit rate to reduce

demand for its deposits. The decline in the deposit rate decreases domestic

and foreign deposit demand and it increases borrowing by impatient house-

holds.

4.3.8 Calibration

Table 4.2 specifies the parameter settings. Patient and impatient consumers

have a slightly different discount factor to ensure that impatient house-

holds borrow and that patient households save. The coefficient that determ-

ines the relative risk aversion of households—the substitution elasticity of

consumption—σc is set at 1 ensuring log-utility and the inverse of the elasti-

city of work effort with respect to the wage rate σl = 2 are set at conventional

values, see Christiano et al. (2005). The substitution elasticity of deposits σm


138 Chapter 4



βp Discount factor patient households 0.990βi Discount factor impatient households 0.989θ Share of patient households 0.500η Share of housing in the consumption bundle 0.250γ

pl Weight of leisure in utility function patient households 0.627

γil Weight of leisure in utility function impatient households 1.920

γm Weight of deposits in utility function 0.040α Share of labor in the production function 0.667δ Capital depreciation rate 0.025φ Capital adjustment costs 2.500σc Substitution elasticity consumption 1.000σm Substitution elasticity deposits holdings 1.000σl Substitution elasticity leisure 2.000H Housing supply 1.000ϑ Exogenous foreign deposit demand 10.000ϕι

1 Market depth feedback parameter 0.200ϕι

2 Shadow bank deposits feedback parameter 0.200πg Productivity good state 1.100πb Productivity bad state 0.850πd Productivity disaster state 0.100P(u) Probability good signal 0.750P(u|H) Probability good state if good signal 0.950P(u|L) Probability good state if bad signal 0.800P(d|L) Probability disaster state if bad signal 0.100ρm Persistence parameter increase in deposits shock 0.900µm Mean increase in deposits shock 0.000σm S.D. savings glut shock 1.000



is set at 1 which also ensures log-utility, but more importantly, a direct link

with consumption. Moreover, we set the weight of housing in the consump-

tion bundle (1− η) equal to 0.25 which entails that housing is 1/4 of total

consumption expenses. The weights of labor and deposits γl and γm in the

utility function are used to normalize labor supply in steady state of both

representative households to unity and bank leverage in steady state equal

to Q/(Q + M) = 20%.

The physical capital adjustment cost parameter φ is set at 2.5, close to the

value estimated by Christiano et al. (2005). The physical capital depreciation

rate δ and the share of labor in the production function α take their standard

values of 0.025 per quarter and 2/3, respectively. The loan-to-value paramet-

ers ζ f and ζe are set equal to unity in the benchmark case. Housing supply

H is fixed to unity. The supply elasticity of foreign deposit demand with

respect to the domestic deposit rate ϑ equals its domestic value in steady

state.

The probabilities that a state of the world occurs and the corresponding

productivities are set such that the ex-ante expected value of Et(πs) equals

1. The expected productivity after the bad signal is equal to approximately

90% and the DGS costs are set to approximately 1% of the bank balance

sheet.

4.4 Results

4.4.1 Growth of mortgage loans

Figure 4.9 shows the effects of an exogenous increase in funding on the ag-

gregate bank balance sheet. In this section, we set shadow banks’ costs of

funding equal to regulated banks’ costs of funding by setting the liquida-

tion value equal to a constant κι = πb/(1 + χ)iι∗. The results for the three

cases discussed in Proposition 4.1 are almost identical because the real side

of the economy is similar. The banking structure, however, is slightly differ-

ent which might give rise to a small difference. Specifically, regulated banks

pay DGS costs which reduces the amount of funding that could be used


140 Chapter 4

Figure 4.9. An increase in bank deposits and the real economy

Notes: Impulse responses following an increase in bank deposits, that is, a positive shock toεm

t while the expected asset liquidation values (κet and κ

ft ) remain constant. The increase in

deposits equals 3% of total domestic deposits Mt. Horizontal axis shows quarters. Verticalaxis shows deviations from steady state.

for lending compared to the uninsured shadow banking sector. Second, the

bank equity constraints of the two banking types are slightly different. This

difference marginally impacts their financial structure and it therefore af-

fects the amplification of fluctuations.

The increase in domestic bank deposits raises banks’ holdings of cent-

ral bank deposits contemporaneously. Although domestic banks could also

lend to the foreign banks who face a shortfall, here we assume that domestic

banks do not want to lend to foreign banks because, e.g., they consider for-

eign banks too risky. Banks lower the deposit rate because aggregate bank

deposits increase, while the resulting central bank deposits do not generate

any extra income. Both the mortgage rate and the corporate loan rate follow

the reduction in bank funding costs because banks compete which eventu-

ally equalizes their lending rate to their weighted average costs of funding.



Figure 4.10. An increase in bank deposits and the share of mortgages (%balance sheet)




deposits equals 3% of total domestic deposits Mt. Horizontal axis shows quarters. Verticalaxis shows deviations from steady state. Mortgage loans as % of the aggregate bank balance

sheet are calculated as: B ft

B ft +Be

t+Dt. The mortgage-to-income ratio is calculated as: B f

tWt Li

t+rkt Kt−1

.

Hence, arbitrage and competition ensure that both lending rates fall and

borrowing increases.

Patient and impatient households hold different asset portfolios. Patient

households hold bank deposits, bank equity and houses while impatient

households hold bank deposits, houses and physical capital. The return on

these assets changes which provides an incentive for both types of house-

holds to rebalance their portfolio. The inflow of deposits raises bank lever-

age and therefore the required return on bank equity increases. As the lever-

age constraint is binding, banks induce patient households to rebalance their

portfolio from deposits and housing towards bank equity. This implies that

the return on bank equity increases relative to the expected return on hous-

ing and deposits. Patient households therefore reduce savings, sell part of

their housing stock to the impatient households and convert the proceeds

and some of their deposits into bank equity.


142 Chapter 4

Impatient households do not own—and do not wish to own—bank equity

and are therefore unaffected by changes in the return on bank equity. That

is, the return on bank equity is still below the required return of impatient

households to due their high discount factor. For banks the costs of fund-

ing decreases because the decline in the interest rate on deposits is larger

than the increase in the required return on bank equity. As the weighted

average costs of funding falls, banks increase their lending by lowering the

lending rate on mortgages and corporate loans. When lending rates decline,

impatient households prefer to increase their indebtedness and buy more

houses and physical capital. Impatient households’ demand for houses and

physical capital given limited supply of both assets drives house prices and

physical capital prices up.

The increase in mortgage lending is stronger than the increase in corpor-

ate lending. Figure 4.10 shows that the total amount of mortgage loans as

percentage of the aggregate bank balance sheet increases. To understand this

outcome, Figure 4.11 plots the expected return on physical capital Etrkt+1,

housing Etrht+1 and bank equity Etre

t+1. As lending rates fall, housing

demand by impatient households increases which drives up house prices.

This same mechanism is at work for physical capital: the increase in demand

for physical capital drives up the price of physical capital and thereby the ex-

pected return on physical capital. However, when patient households obtain

funding to increase the production of physical capital, the return on phys-

ical capital falls. For housing demand, no offsetting supply effect is present.

The house price increase relaxes the collateral constraint for mortgage loans

more than the collateral constraint for corporate loans. Consequently, the

supply of mortgage loans can increase by more than the supply of corporate

loans and bank investment is reallocated towards mortgages.

The aggregate housing stock is fixed, but from the perspective of the im-

patient household housing supply increases. This housing supply effect is,

in the model, induced by patient households who sell part of their housing

stock to impatient households. Patient households are willing to do so be-

cause the expected return on bank equity increases even more. These results



Figure 4.11. Expected return on physical capital, housing and bank equityfollowing an increase in bank deposits




deposits equals 3% of total domestic deposits Mt. Horizontal axis shows quarters. Verticalaxis shows deviations from steady state. The expected return to physical capital Etrk

t+1 isrepresented by the circled (black) line, the expected return to housing Etrh

t+1 is representedby the barbed (blue) line and the expected return to bank equity Etre

t+1 is given by the bar-striped (red) line.

imply that both a reduction in the supply elasticity of housing and a de-

crease in the share of households buying a house with their own wealth, in-

creases house price fluctuations and therefore mortgage supply fluctuations.

4.4.2 Shadow bank growth

In this section we link the relative growth of mortgage loans to the growth

rate of the shadow banking sector. In Section 4.4.1 the liquidation value was

set equal to a constant. In the remainder of this chapter, the liquidation value

is endogenously determined by Equation (4.18). Accordingly, the relative

growth of mortgage loans following the decrease in interest rates described

in Figure 4.9 deepens the interbank market for mortgage loans. The expected


144 Chapter 4

Figure 4.12. Expected asset liquidation value following an inflow of deposits

Notes: Impulse responses following an increase in bank deposits, that is, a pos-itive shock to εm

t . Horizontal axis quarters. Vertical axis shows deviations from

steady state. The functional form for the asset liquidation value is: ϕι(

Bιt

Bt, Msb

tMt

)≡(

1 + ϕι1 log

Bι

t

Bιt+Bι′

t

)(− log

ϕι

2 Msbt

Mt

). The barbed (blue) line represents the expected li-

quidation value for mortgage loans (κ ft ) without aggregate liquidity risk (ϕ

f1 = 1 and the

second term in round brackets on the right hand side equals 1). The circled (black) linesrepresented the expected liquidation value for mortgage loans with high aggregate liquidityrisk (ϕ

f1 = 1 and ϕ

f2 = 6). The bar-striped (red) line shows the expected liquidation value for

corporate loans (κet ) without aggregate liquidity risk (ϕe

1 = 1 and the second term in roundbrackets on the right hand side equals 1).

liquidation value κft increases which improves the comparative advantage

of shadow banks vis-a-vis regulated banks in supplying mortgage loans.

Positive feedback between the size of the shadow banking sector and

the asset liquidation value, ∂κ f /∂Bι > 0, allows the shadow banking sector

to grow. Specifically, more investment in mortgage loans by shadow banks

increases the size of and thereby liquidity in the interbank market for mort-

gage loans. This increases the expected asset liquidation value and therefore

the amount of uninsured deposits shadow banks can create by creating new

loans. In equilibrium, this positive feedback between the size of the interb-

ank market and the expected liquidation value internalizes the externality:

∂κι/∂Bι → 0.



The barbed line in Figure 4.12 shows that the market for mortgage loans

becomes more liquid—the expected liquidation value for shadow bank as-

sets increases—when banks receive an inflow of deposits. Even though shadow

banks do not take the effect of their own behavior on the assets’ liquidation

value into account, liquidity in the market is improving. The comparative

advantage of shadow banks with respect to supplying mortgages increases.

The dotted line in Figure 4.12 shows how liquidity in the interbank mar-

ket for corporate loans is decreasing, compared to the interbank market for

mortgages, because the market for corporate loans is shrinking. Hence, an

exogenous inflow of deposits in banks increases liquidity in the market for

mortgage loans. This in turn fosters the comparative advantage of shadow

banks over regulated banks.

4.4.3 Liquidity risk and the lender of last resort

In the model, liquidity risk in the banking sector depends on the size of the

shadow banking sector. When a pessimistic signal occurs, two things can

happen. First, if the shadow banking sector is relatively small compared to

the regulated banking sector,(

Msbt /Mt ≈ 0

), the interbank market contin-

ues to function efficiently as only a small share of the banking sector sells

assets. In this case the regulated banking sector buys—or lends the funding

shortfall to—the shadow banking sector. Regulated bank deposits increase

and aggregate liquidity is unaffected because households do not increase

their holdings of cash: Mcbt = 0 and ∆Mrb

t = ∆Msbt .

Second, if the shadow banking sector is relatively large(

Msbt /Mt ≈ 1

),

a large share of the interbank market starts to sell assets. Without sufficient

activity in the interbank market regulated banks cannot diversify their as-

sets and/or insure idiosyncratic liquidity risks. It becomes increasingly diffi-

cult for regulated banks to guarantee the safety and liquidity of their depos-

its. Regulated bank deposits might therefore be converted into cash: Mcbt > 0

and ∆Msbt > ∆Mrb

t . In this case, aggregate liquidity decreases and regulated

banks need additional funding from the central bank.

Regulated banks can borrow from the central bank or reduce their lend-


146 Chapter 4

ing to the central bank to compensate for the decrease in depository fund-

ing. When households increase their holdings of cash, the liability side of the

central bank balance sheet increases, see Equation (4.26). The central bank

balance sheet implies that either central bank deposits Rt should decrease

or bank borrowing from the central bank Bcbt should increase. However, for

regulated banks to have a level of central bank deposits Rt > 0, they must

have borrowed from the central bank in the first place Bcbt = Rt. In this case,

∆Mcbt = −∆Rt. In steady state banks do not borrow from the central bank to

hold (costly) central bank deposits in excess of any requirement. Therefore

Rt cannot decrease to compensate for the deposit outflow. Alternatively, bor-

rowing from the central bank must increase ∆Bcbt = ∆Mcb

t . In other words,

by providing cash to households via the banking sector, the central bank

must also provide liquidity insurance to banks.

In practice, the central bank lends to regulated banks if they have ad-

equate collateral. There is no need to internalize the increase in liquidity risk

if the market expects that the central bank will always lend to the regulated

banking sector because they have sufficient adequate collateral. The central

bank is the lender of last resort and can provide regulated banks additional

funding equal to: ∆Bcbt = ∆Msb

t − ∆Mrbt . Buying shadow bank assets poses

no threat to the regulated banks’ future funding position, if they can always

borrow from the central bank. Regulated bank deposits remain safe and li-

quid and depositors are unlikely to convert their regulated bank deposits

into cash. Hence, the risk associated with the creation of uninsured shadow

bank deposits, ∂κιt/∂Ms

t , depends on whether the central bank is likely to

lend to regulated banks.

A growing shadow banking sector increases the regulated banks’ reli-

ance on liquidity support by the central bank. Yet, regulated banks do not

pay a fee for this liquidity insurance. Although it becomes more likely that

the central bank must provide liquidity support when the shadow banking

sector grows, the costs of liquidity support by the central bank are unaf-

fected. In contrast, borrowing from the central bank is even likely to become

less expensive if the central bank is expected to lower the policy rate in re-



sponse to a financial crisis. Also, as has been the case during the global finan-

cial crisis, the central bank might accept a broader set of assets as collateral

when all banks have a funding shortness. Consequently, shadow banks cre-

ate too many uninsured deposits compared to the social optimum, i.e., they

expose the banking system to excessive liquidity risk, because liquidity in-

surance by the central bank is not priced.

In this case, the increase in market liquidity as a consequence of a deeper

interbank market outweighs the increase in funding liquidity risk as the lat-

ter effect is not fully priced. The barbed line in Figure 4.12 shows that the

expected asset liquidation value increases and the shadow bank equity con-

straint (4.17) is relaxed when shadow bank lending increases because the

actual increase in liquidity risk is not internalized. The circled line in Figure

4.12 shows how liquidity in the market for mortgages actually decreases

when the increase in liquidity risk is internalized. The difference between

the barbed and the circled line represents the value of the liquidity insur-

ance provided by the central bank.

4.5 Policy options

4.5.1 Loan-to-value constraints

A reallocation of bank investment towards mortgage loans can adversely

impact economic growth and financial stability. Such a reallocation does not

depend on the financial structure of the banking sector and is not associ-

ated with an externality. In fact, the reallocation is determined by limited

housing supply and the collateral constraints for both mortgage loans and

corporate loans work, if anything, in the opposite direction limiting credit

supply. However, an increase in household debt relative to income makes it

harder to repay the debt. Indeed, Figure 4.10 shows that the loan is financed

to a larger extent by an increase in collateral value and not by an increase

in household income. Although the model excludes actual Ponzi schemes

by construction, in practice it might be harder to distinguish an increase in

mortgage debt supported by fundamentals from an increase in household


148 Chapter 4

Figure 4.13. An increase in bank deposits and restrictions on admissibleloan-to-value ratios


t . Restrictions on admissible loan-to-value ratios, circled (black) line LTV is 100% (ζ f = 1)and barbed (red) line LTV is 80% (ζ f = 0.8). Horizontal axis quarters. Vertical axis showsdeviations from steady state.

debt supported by Ponzi finance (Minsky, 1986).

Prudential authorities in some countries have recently responded to the

increase in household debt relative to household income and/or house value

by introducing restrictions on admissible loan-to-value (LTV) and loan-to-

income ratios. These restrictions should create a precautionary buffer against

house price fluctuations. From Equations (4.10) and (4.11) and the analysis

in Appendix 4.B, we conclude that the steady-state loan-to-value-ratio falls

when these constraints tighten. A lower LTV ratio provides a buffer against

future house price fluctuations.

Figure 4.13 reveals two additional benefits of restrictions on admissible

LTV ratios. First, stricter constraints on admissible LTV ratios limit house

price and thereby mortgage supply fluctuations when shocks hit the eco-



nomy. Although the restrictions by themselves are not sufficient to prevent

the reallocation of investment and thereby shadow banking growth, they do

attenuate bank investment in mortgage loans and thereby shadow banking

growth. Hence, restrictions on admissible LTV ratios provide a larger buffer

against house price fluctuations, and simultaneously attenuate fluctuations

in house prices and mortgage loans. Second, restrictions on admissible LTV

ratios reallocate bank investment from mortgage loans to corporate loans.

This effect is not only present in the steady state but also when credit sup-

ply expands. As less lending are re-allocated towards houses, the fall in in-

terest rates following the inflow of deposits has a stronger positive effect

on investment. Hence, restrictions on admissible LTV ratios can reallocate

investment to physical capital while it limits household mortgage debt and

house price growth.

4.5.2 Interest on cash

The increase in liquidity risk due to the creation of uninsured shadow bank

deposits is, if not internalized by the banks, a pecuniary externality and

socially excessive. Pecuniary externalities violate the first welfare theorem

when the liquidation value affects not only the bank’s budget constraint, but

also its collateral constraint. As the liquidation price is present in the bank

equity constraint, the first welfare theorem is violated. The growth of mort-

gage debt increases regulatory arbitrage, but the banking sector does not

price the increase in liquidity risk associated with more uninsured shadow

bank deposits. The shadow banking sector creates too many uninsured de-

posits compared to the social optimum which leaves the financial system

excessively vulnerable to a liquidity crisis.

The key externality driving a wedge between private and social optimal

values is the negligence of an increase in liquidity risk when shadow banks

create uninsured deposits. As the creation of insured deposits creates liquid-

ity risk, the central bank provides liquidity insurance. However, since li-

quidity insurance is not priced, banks issue too many deposits rather than

equity leaving the financial sector vulnerable to liquidity crises. A deposit


150 Chapter 4

insurance scheme reallocates the risk of creating uninsured deposits outside

the regulated banking sector towards the shadow banking sector. This how-

ever, does not solve the financial systems’ reliance on liquidity insurance

provided by the central bank.

Central banks can realign private and social interests by regulating the

total amount of (uninsured) bank deposits. One possibility is a Pigouvian

tax as suggested by Stein (2012). In his proposal the central bank regulates

the total amount of private uninsured deposit creation by introducing a flex-

ible cap-and-trade system in which banks are granted tradable permits to

create uninsured deposits. The price of these permits reveals information

about the banking sectors’ investment opportunities. The regulator can ad-

just the amount of permits in the system in accordance with its objectives

when prices change.

Although the cap-and-trade system proposed by Stein (2012) is an effect-

ive instrument to regulate the creation of uninsured deposits by regulated

banks, it has adverse consequences on shadow banks and the real economy.

For one thing, the system does not allow the regulator to observe the op-

timal level of permits. When the price of permits increases, the banking sec-

tor might have better investment opportunities, but it does not signal how

much investment is optimal. Moreover, restricting the creation of uninsured

deposits increases regulatory arbitrage as deposits become more scarce. Ac-

cordingly, shadow banks, who are not regulated, have a larger incentive to

create uninsured deposits while any liquidity risk remains insured by the

central bank. The cap-and-trade system therefore does not eliminate the key

externality, but relocates risks outside the regulated banking sector.

Here, we suggest a more direct approach: the central bank pays interest

on cash. Thereby the central bank eliminates the incentive for both regulated

banks and shadow banks to create uninsured deposits. The basic idea is

that paying interest on cash raises the opportunity costs for households to

deposit their savings in regulated and shadow banks. If the interest rate on

cash is set higher than the interest rate on bank deposits, banks must raise

the deposit rate to attract depository funding thereby reducing the incentive



to finance themselves with deposits rather than equity.

Deposits can be used for consumption while equity cannot. From the

patient households’ FOC with respect to deposits and after substituting the

FOC with respect to bank equity, we can induce that households are willing

to pay a premium for deposits relative to equity:

(Mjt)

σm=

γm

λpt

(1 + iq

t

iqt − im

t

). (4.27)

From (4.27) we find that if deposit demand is positive, the rate on deposits

is lower than the required return on equity: iqt > im

t . Consequently, banks

have an incentive to finance themselves with deposits rather than equity.

Cash can also be used for consumption, but households limit their hold-

ings of it because cash does not pay interest. We therefore propose that the

central bank pays interest on cash to compete with the banking sector in

the creation of liquid, safe claims. In the initial case where the central bank

pays no interest im,cbt = 0, households will only hold cash for consumption

purposes when no alternative is available. If the central bank pays interest

on cash which is higher than the interest rate on bank deposits im,cbt > im,s

t ,

depositors would like to hold only cash and no bank deposits. In this case,

both types of banks must raise the deposit rate to retain their deposits, fin-

ance themselves fully with equity or borrow from the central bank for the

same rate: im,cbt . Consequently, when im,cb

t = iqt banks become indifferent

between debt and equity finance as both have exactly the same costs. That

is, the Modigliani and Miller (1958) irrelevance proposition is no longer vi-

olated.

In practice the central bank can set the interest rate on central bank de-

posits equal to the interest rate banks receive on their deposits at the cent-

ral bank. At this interest rate the externality associated with the creation of

uninsured deposits is eliminated. In the model presented in this chapter,

the (risk-free) required return on bank equity is equal to the interest rate

banks receive on their deposits at the central bank. The deposit rate trades

at a discount of this rate as consumers are willing to accept a lower interest


152 Chapter 4

rate for liquid and safe deposits (the literature refers to this difference as

the money premium). The difference between the policy rate and the de-

posit rate stimulates banks to finance themselves with deposits rather than

equity. Hence, if the central bank offer households a savings account that

pays an interest rate equal to the interest rate banks receive on their deposits

at the central bank, this difference disappears. Depositors become indiffer-

ent between central bank deposits and bank deposits while banks become

indifferent between deposit and equity finance.

4.6 Conclusion

In this chapter we showed how an exogenous decline in real interest rates

caused by an inflow of deposits could explain both the reallocation of bank

investment from corporate loans to mortgages and the growth of the shadow

banking sector relative to the regulated banking sector. Specifically, inelastic

housing supply relative to the supply of physical capital causes house prices

to rise which relaxes the collateral constraint for mortgage debt and induces

the reallocation, in relative terms, towards mortgage loans. Positive feed-

back between the depth of the interbank market for mortgage loans and the

liquidation value of shadow bank assets increases shadow banks’ compar-

ative advantage over regulated banks in supplying mortgages.

In the model we showed that the growing shadow banking sector leaves

the banking sector excessively vulnerable to financial crises. When shadow

banks grow and they finance their loans with uninsured deposits, liquid-

ity risk increases. The shadow banking sector relies indirectly on liquid-

ity insurance provided by the central bank. As shadow banks create more

uninsured deposits, the banking system’s reliance on liquidity support by

the central bank increases. However, liquidity insurance is not priced in

the market. The increase in liquidity risk is therefore not fully incorpor-

ated in the expected liquidation price of shadow bank assets. Consequently,

shadow banks issue too many uninsured deposits relative to the social op-

timum.



Macroprudential regulation—such as restrictions on admissible loan-to-

value ratios—can offer a first line of defense to preserve financial stability

because these constraints re-allocate bank investment back towards corpor-

ate loans. In addition, central banks can remove the incentive for banks to

finance themselves with deposits rather than equity by paying interest on

cash. Thereby the central bank raises the households’ opportunity costs of

holding bank deposits. Banks must increase the deposit rate which reduces

the incentive for banks to finance themselves with deposits rather than bank

equity. This eliminates a key externality and leaves the economy less vulner-

able to liquidity risk.

4.A Variable names and definitions

Table 4.A.1. Variable names and definitions

Notation Source Definition

Shadow bank growth ∆ ln Ysbt Flow of funds ∆ log of other financial inter-

accounts FRB US mediaries except insurance companiesand pension funds; total financial assets

Regulated bank growth ∆ ln Yrbt Flow of funds ∆ log of domestic financial

accounts FRB US sectors; total financial assetsGrowth of mortgage loans ∆ ln Mtotal

t Flow of funds ∆ log all sectors;accounts FRB US total mortgages; asset

Growth of mortgage loans ∆ ln Mpdit Flow of funds ∆ log private depository

(only depository institutions) accounts FRB US institutions; total mortgages; assetGrowth of corporate loans ∆ ln Ctotal

t Flow of funds ∆ log nonfinancial corporateaccounts FRB US business; loans; liability

MBS and ABS markets growth ∆ ln Ztotalt Flow of funds ∆ log of total GSE

accounts FRB US ABS and private MBS marketsInflation (CPI) - Federal Reserve Consumer Price Index for All Urban

Bank of St. Louis Consumers: All Items, Percent Changefrom Year Ago, Quarterly, Seasonally Adj.

Federal Funds Rate - Federal Reserve Effective Federal Funds Rate, Percent,Bank of St. Louis Quarterly, Not Seasonally Adj.

GDP growth - Federal Reserve Real Gross Domestic Product, PercentBank of St. Louis Change from Preceding Period, Quarterly,

Seasonally Adjusted Annual Rate


154 Chapter 4

Table 4.A.2. Descriptive statistics

Mean Median Maximum Minimum Std. Dev. Jarque-Bera Obs.

Shadow bank growth 10.699 11.655 29.978 -9.868 6.688 16.839 248Regulated bank growth 6.978 7.231 14.416 -6.480 3.484 19.192 248Growth of mortgage loans 7.784 8.760 14.423 -4.142 4.337 30.938 248Growth of mortgage loans 7.148 7.844 16.808 -6.703 5.328 16.124 248(private depository institutions)Growth of corporate loans 6.716 8.408 21.250 -22.023 7.316 129.442 248MBS and ABS markets growth 12.594 12.735 39.739 -17.791 9.561 1.072 248Inflation (CPI) 3.656 3.032 14.426 -1.607 2.817 179.824 248Federal Funds Rate 4.949 4.750 17.780 0.070 3.593 47.745 248GDP growth 3.059 3.050 16.500 -10.000 3.550 27.011 248

Figure 4.A.1. VAR estimation results of Equation (4.2) for shadow banks dif-ferent ordering

Corporate loan to shadow bankCorporate loan to mortgage loan Corporate loan to corporate loan


Shadow bank to shadow bankShadow bank to mortgage loan Shadow bank to corporate loans

Mortgage loan to shadow bankMortgage loan to mortgage loan Mortgage loan to corporate loan

-2

-1

0

1

2

2 4 6 8 10

-2

-1

0

1

2

2 4 6 8 10

-2

-1

0

1

2

2 4 6 8 10

-2

0

2

4

2 4 6 8 10

-2

0

2

4

2 4 6 8 10

-2

0

2

4

2 4 6 8 10

-2

0

2

4

2 4 6 8 10

-2

0

2

4

2 4 6 8 10

-2

0

2

4

2 4 6 8 10

Notes: Ordering Xt = [Mtotalt , Ctotal

t , Ybt , Breal

t , Ztotalt ]. Estimation period 1955Q3–2017Q2,

time (quarters) horizontal axis, percentage point deviation on the vertical axis. The titlesexplain the response of one of the variables included to a shock of any of the variables in-cluded. Dotted red lines denote confidence intervals at 95% significance level.



4.B Household and firm problem

Patient household problem

Patient household utility function:

U jt = Et

∞

∑t=0

(βj)tεjt

(((Cj

t)η(H j

t)1−η)1−σc

1− σc + γm (Mjt)

1−σm

1− σm − γl (Ljt)

1+σl

1 + σl

).

(4.B.1)

Patient household budget constraint:

Mpt + Qt + qh

t (Hpt − Hp

t−1) =(1 + imt−1)Mp

t−1 + (1 + iqt−1)Qt−1 + rh

t Hpt−1

− Cpt + Ltwt + θ(Πtb

t + Πpt ). (4.B.2)

Patient household Lagrangian:

Lp =E0

∞

∑t=0

(βp)t εpt

(((Cp

t )η(Hp

t )1−η)1−σc

1− σc + γm (Mpt )

1−σm

1− σm − γl (Lpt )

1+σl

1 + σl

)

+ λpt

[(1 + im

t−1)Mpt−1 + (1 + iq

t−1)Qt−1 + rht Hp

t−1 + Ltwt

+ θ(Πtbt + Πp

t )− Cpt − It −Mp

t −Qt − qht (Hp

t − Hpt−1)

], (4.B.3)

where λpt is the Lagrangian multiplier associated with the patient household

budget constraint. The FOCs conditions w.r.t. Cpt , Lp

t , Hpt , Mp

t , Qt are given

by:

ηCp(η−1)t (Cpη

t Hp(1−η)t )−σc

= λpt (4.B.4)

εpt γl(Lp

t )σl= λ

pt wt (4.B.5)

εpt (1− η)Hp(−η)

t (Cpηt Hp(1−η)

t )−σc − λpt qh

t + λpt+1βp(qh

t+1 + rht+1) = 0

(4.B.6)

εpt γm(Mj,ι

t )−σm+ λ

pt+1βp(1 + im

t ) = λpt (4.B.7)

λpt+1βp(1 + iq

t ) = λpt . (4.B.8)


156 Chapter 4

Rewriting the FOCs, substituting out the Lagrangian multipliers λpt and

setting σc = 1 gives the patient household Euler Equation:

Cpt = Et

(Cp

t+1

βp(1 + iqt )

)(Hp

t+1

Hpt

)(1−η), (4.B.9)

and patient household housing demand:

1

Hpt Cjη

t

=

(η

1− η

)(Ph

t

Cpt Hp(1−η)

t

−βp(Ph

t+1 + rht+1)

Cpt+1Hp(1−η)

t+1

), (4.B.10)

and patient household money demand:

Cpt Hp(1−η)

t

(Mjt)

σm=

η

γm

(1− 1 + im

t

1 + iqt

). (4.B.11)

Impatient household Problem

Impatient household Lagrangian:

Li =E0

∞

∑t=0

(βi)t(

((Cit)

η(Hit)

1−η)1−σc

1− σc + γm (Mit)

1−σm

1− σm − γl (Lit)

1+σl

1 + σl

)+

λit

[(1 + i f

t−1)B ft−1 + (1 + ie

t−1)Bet−1 − (1 + im

t−1)Mit−1 − rh

t Hit−1 − wtLi

t−

rkt Kt − (1− θ)(Πtb

t + Πpt ) + Ci

t + It − B ft − Be

t + Mit + qh

t (Hit − Hi

t−1)

]−

λitq

kt

[Kt(1− δ) + It

(1− φ

2

(It

It−1− 1)2 )

− Kt+1

]+

µet

(B

e

t − qkt Kt

)+

µft

(B

f

t − qht Ht

). (4.B.12)

where λit is the Lagrangian multiplier associated with the impatient house-

hold budget constraint, qkt is the shadow value of physical capital associated

with the physical capital accumulation identity and µet and µ

ft denote the



shadow value of the loan-to-value constraints. The FOCs w.r.t. Kt, It, B ft , Be

t ,

Cit, Hi

t, Mpt , Lp

t :

λitq

kt =λi

t+1rkt+1 + λi

t+1qkt+1(1− δ) + qk

t+1µet+1 (4.B.13)

λit =λi

tqkt

(1− φ

2

(It

It−1− 1)2

− φ

(It

It−1− 1)(

It

It−1

))+

λit+1qk

t+1βj

(φ

(It+1

It− 1)(

It+1

It

)2)

(4.B.14)

λit =λi

t+1βi(1 + i ft ) + µ

ft (4.B.15)

λit =λi

t+1βi(1 + iet) + µe

t (4.B.16)

λit =ηCi(η−1)

t (Ciηt Hi(1−η)

t )−σc(4.B.17)

λitq

ht =(1− η)Hi(−η)

t (Ciηt Hi(1−η)

t )−σc+ λi

t+1βi(qht+1 + rh

t+1) + µft qh

t

(4.B.18)

γm

(Mit)

σm =λit

(1− 1 + im

t1 + ie

t

)+ µe

t

(1 + im

t1 + ie

t

), (4.B.19)

γl(Lit)

σl=λi

t+1W it . (4.B.20)

Rewriting the FOCs, substituting out the Lagrangian multiplier λit and

µft and setting σc = 1 gives the patient household Euler Equation:

1

Ciηt Hi

t

=

(η

1− η

)[qh

t

CitH

i(1−η)t

−βi(qh

t+1 + rht+1)

Cit+1Hi(1−η)

t+1

+

qht

(βi(1 + i f

t )

Cit+1Hi(1−η)

t+1

− 1

CitH

i(1−η)t

)](4.B.21)

and money demand:

CitH

i(1−η)t

(Mit)

σm =η

γm

(1− 1 + im

t

1 + i ft

)+ µ

ft

(1 + im

t

1 + i ft

). (4.B.22)


158 Chapter 4

Firm Problem

Firm Lagrangian:

L f = rkt Kt−1 + wtLt − λ

ft

(Et(πs)At(Kt−1)

1−α(Lt)α −Yt

), (4.B.23)

where λft denotes firms’ marginal costs which are in a competitive environ-

ment equal to the price level. We obtain the following FOCs w.r.t. Kt−1 and

Lt:

rkt =

(1− α)Yt

Kt−1(4.B.24)

wt =αYt

Lt(4.B.25)

Assuming free-entry and exit, firms will enter until expected economic profits

are zero. Accordingly, firm profits:

Πt = Et(πs)(Yt −Wt(Lpt − Li

t)− rkt Kt), (4.B.26)

will be equal to zero.

4.C Bank optimization problem

The bank maximizes its profits subject to its budget constraint and equity

buffer constraint:

max(Etπs[(1 + i f

t )B f ,tbt + (1 + ie

t)Be,tbt ]− im,tb

t Mtbt − iq,tb

t Qtbt − B f ,tb

t −

Be,tbt − χ((1 + i f

t )B ft + (1 + ie

t)Bet )

−

λtbt (Be,tb

t + B f ,tbt + χ((1 + i f

t )B ft + (1 + ie

t)Bet )−Qtb

t −Mtbt )

µtbt ((1 + im,tb

t )Mtbt − πb[(1 + i f

t )B ft + (1 + ie

t)Bet ]), (4.C.27)

where λtbt and µtb

t are the Lagrangian multipliers associated with the budget

constraint and equity buffer constraint respectively. The FOCs w.r.t. B f ,tbt ,



Be,tbt , Mtb

t , Qtbt are denoted by:

i ft =χ(1 + i f

t ) + λtbt (1 + χ(1 + i f

t )) + µtbt πb(1 + i f

t ), (4.C.28)

iet =χ(1 + i f

t ) + λtbt (1 + χ(1 + ie

t)) + µtbt πb(1 + ie

t), (4.C.29)

im,sbt =λtb

t + µtbt (1 + im,tb

t ), (4.C.30)

iq,sbt =λtb

t . (4.C.31)

From the FOCs we get that the shadow value with respect to the budget

constraint λtbt = iq,sb

t > 0. Consequently, we know that the budget constraint

holds with equality. Next we can combine the FOCs w.r.t. Mtbt and Qtb

t to

obtain: µtbt =

(im,sbt −iq,sb

t

1+im,tbt

). From the household problem we know that im,sb

t <

iq,sbt if γm > 0, i.e., when households value money, the bank equity buffer

constraints holds with equality. Combining the FOCs we obtain:

i ft − χ(1 + i f

t ) =λtbt (1 + χ(1 + i f

t )) + µtbt πb(1 + i f

t ), (4.C.32)

iet − χ(1 + i f

t ) =λtbt (1 + χ(1 + ie

t)) + µtbt πb(1 + ie

t). (4.C.33)

We can interpret these results as follows. Traditional banks will increase in-

vestment in either asset as long as the budget constraints and the equity

buffer constraints do not bind. It is possible to substitute the budget and

equity buffer constraints in the maximization problem to obtain:

max

Etπs[(1 + i ft )B f ,tb

t + (1 + iet)Be,tb

t ]− (4.C.34)

πb[(1 + i ft )B f

t + (1 + iet)Be

t ]− (1 + iq,tbt )Qtb

t

.

From this we know that as long as the return on a particular asset is larger

than the costs of deposit insurance and equity, traditional banks increase in-

vestment. Hence, the equity buffer constraint determines the amount of de-

posits, the credit supply curve is flat for lending rates larger than the costs of

deposit insurance and equity, and bank equity is determined as the residual

from the balance sheet identity.


160 Chapter 4

For shadow banks the problem is similar:

max(Etπs[(1 + i f

t )B f ,sbt + (1 + ie

t)Be,sbt ]− im,sb

t Msbt − iq,sb

t Qsbt − B f ,sb

t −

Be,sbt

− λsb

t (Be,sbt + B f ,sb

t −Qsbt −Msb

t )

µsbt ((1 + im,s

t )Mst − ν[k f

t (1 + i ft )B f

t + ket(1 + ie

t)Bet ]) (4.C.35)

where ν ≡ [P(d|H)πg + (1− P(d|H) − P(d|L))πb + P(d|L)πd]. The FOCs

w.r.t. B f ,sbt , Be,sb

t , Msbt , Qsb

t are denoted by:

Etπs(1 + i ft )− 1 = λsb

t + µsbt νk f

t (1 + i ft ) (4.C.36)

Etπs(1 + iet)− 1 = λsb

t + µsbt νke

t(1 + iet) (4.C.37)

im,sbt = λsb

t + µsbt (1 + im,sb

t ) (4.C.38)

iq,sbt = λsb

t . (4.C.39)

From the FOCs wrt Mtbt and Qtb

t we obtain again λsbt > 0 and µsb

t > 0 and so

both constraints hold with equality. Substituting out the multipliers gives:

Etπs(1 + i ft )− 1 =iq,sb

t +

(1 + i f

t

1 + im,sbt

)νk f

t (im,sbt − iq,sb

t ) (4.C.40)

Etπs(1 + iet)− 1 =iq,sb

t +

(1 + ie

t

1 + im,sbt

)νke

t(im,sbt − iq,sb

t ) (4.C.41)

and similar to the traditional banking problem we can substitute the con-

straints in the profit function to obtain:

max(Etπs[(1 + i f

t )B f ,sbt + (1 + ie

t)Be,sbt ]− ν[k f

t (1 + i ft )B f

t +

ket(1 + ie

t)Bet ]− (1 + iq,sb

t )Qsbt

(4.C.42)

From this we know that as long as the return on a particular asset is larger

than the expected liquidation costs and equity, traditional banks increase

investment. Hence, similar to traditional banks the equity buffer constraint



determines the amount of deposits, the credit supply curve is flat for lending

rates larger than the costs liquidation insurance and equity, and bank equity

is determined as the residual from the balance sheet identity.

4.D Proof Proposition 4.1

For shadow banks the weighted average costs of funding is denoted by:

isbt =

qsbt

qsbt + msb

tiqt +

msbt

qsbt + msb

timt . (4.D.43)

Using the shadow bank balance sheet constraint (4.15) and the shadow bank

equity buffer constraint for asset ι (4.17):

isbt = iq

t +πb[κ

ιt(1 + iι

t)bιt]

bιt(1 + im

t )

(imt − iq

t)

. (4.D.44)

For traditional banks the weighted average costs of funding are:

itbt =

qtbt

qtbt + msb

tiqt +

mtbt

qt + mtbt

imt . (4.D.45)

Using the traditional bank balance sheet constraint (4.15) and the traditional

bank equity buffer constraint (4.16) :

itbt = iq

t +πb[(1 + iι

t)bιt]

(1 + imt ) (1 + χ) bι

t

(imt − iq

t)

. (4.D.46)

Equating the marginal costs of shadow banks (4.D.44) with the marginal

costs of traditional banks (4.D.46) to determine which banking sector has

higher marginal costs we obtain that both banking sectors have the same

marginal costs if:

11 + χ

= κιt. (4.D.47)


162 Chapter 4

From this we can conclude that both banks invest in both assets if:

11 + χ

= κet = κ

ft . (4.D.48)

Traditional banks invest only in corporate loans assets and shadow banks

invest only in mortgage loans if:

11 + χ

> κet and

11 + χ

< κft (4.D.49)

Traditional banks invest only in mortgage loans and shadow banks invest

only in corporate loans if:

11 + χ

< κet and

11 + χ

> κft . (4.D.50)

4.E Including idiosyncratic credit risk

In the main text we argued that both traditional and shadow banks always

completely diversify their portfolios if they have the opportunity to do so.

To diversify all idiosyncratic risk the bank must trade with other interme-

diaries as they are not able to completely diversify idiosyncratic risk by

themselves because it is, for example, costly (see Hanson et al. (2015)). To

diversify the risk of these projects, both types of banks trade in the interb-

ank market. Specifically, they sell Sι,it units of risky projects and they buy Bι,i

t

units of risky projects financed by other banks. Consequently, the actuarially

fair priced deposit guarantee system is expressed as:

Dt =

[P(d)P(d|L)(1− πd) + (P(d)(1− P(d|L)− P(u|L))+

P(u)P(u|H))(1− πb) + (P(u)P(u|H) + P(d)P(u|L)(1− πg)]πb+

P(d)P(d|L)πd(πb − πd)

]πb[(1 + iι

t)(I ιt − Sι

t))]+

P(d)P(d|L)[(1 + iιt)Bι

t](πb − πd), (4.E.51)



which states that the deposit insurance premium consists of two parts. The

first part calculates the probability of failure for the bank’s own investment

projects which are subject to both idiosyncratic and aggregate risk (I ιt − Sι

t),

see Figure 4.8 for the probabilities of these projects defaulting. Second, the

bank also owns (potentially) diversified securities Bιt. These securities are

not subject to idiosyncratic risk, but only to aggregate risk. The deposit in-

surance in this case only needs to cover the difference between the bad and

disaster state. Diversification lowers the premium paid for deposit insur-

ance and therefore allows traditional banks to invest more in the risky asset.

So, diversification allows banks to attract more deposits for a given amount

of equity. Therefore traditional banks will always completely diversify their

portfolio if diversification costs are sufficiently low.

Shadow banks do not gain directly from diversification. The shadow

bank equity buffer constraint is specified by:

[P(u|L)πg + (1− P(u|L)− P(d|L))πb+

P(d|L)πd][kιt(1 + iι

t)(I ιt + Bι

t − Sιt)] ≥ (1 + im,s

t )Mst , (4.E.52)

from which we learn that shadow banks do not gain directly from diversi-

fication as it does not impact the fundamental value of the asset. It is best to

read the participation constraint as a “worst case scenario outcome” which

is the occurrence of a pessimistic signal. Diversification does not matter as

it does not allow shadow banks to create additional risk-free debt claims.

However, shadow banks liquidate all their assets in case a signal about the

future state of the world is pessimistic. Traditional banks buy these assets,

but only if the price of the securities is fair:

κιt = (1− χ)

(Et|S′=L(πs)

)ϕι

1

(Bι

tBt

)ϕι

2

(Msb

tMt

), (4.E.53)

where χ is the DGS premium described by (4.E.52). It is evident from (4.E.52)

and (4.E.53) that χ is larger if the shadow banks sell non-diversified assets.

Consequently, the liquidation value is in expectation lower when shadow


164 Chapter 4

banks have a non-diversified portfolio. For this reason, shadow banks also

diversify their portfolio completely when diversification costs are sufficiently

low.

If we assume a symmetric equilibrium (all banks are alike), S f ,it = B f ,i

t

and Se,it = Be,i

t so we can conclude that I f ,it = S f ,i

t = B f ,it and Ie,i

t = Se,it = Be,i

t

and we obtain the diversified optimization problem stated in the main text.


Chapter 5

Sectoral allocation and

macroeconomic imbalances in

EMU∗

5.1 Introduction

In the run-up to the introduction of the euro, both real and nominal interest

rates in the Southern members of the Economic and Monetary Union (EMU)

decreased markedly. This induced major capital flows from the North to

the South, which were initially considered to be largely benign.1 In retro-

spect however, the inflow of capital mainly fueled a boom of domestic lend-

ing and construction, contributing little to productivity growth or business

cycle convergence.2 As the discrepancy between the external debt level and

the capacity to repay kept growing, eventually the solvency of the recipient

regions came under pressure (see Giavazzi and Spaventa, 2010). Whereas

∗This chapter is based upon Gilbert and Pool (2016).1 See for instance Feldstein (2012) who describes the large intra-EMU capital flows and Blan-

chard and Giavazzi (2002) for a—at that time—common interpretation of these capital flows.2 Comunale and Hessel (2014) describe how the surge in domestic demand was the rooSt

cause behind the emergence of current account deficits. Fagan and Gaspar (2007) show thatcapital inflows fueled a consumption boom while Eichengreen (2010) and Holinski et al.(2012) show that the Southern countries became relatively less productive after monetaryintegration.


166 Chapter 5

there exists a fairly broad consensus regarding this narrative (see e.g. Bald-

win and Giavazzi, 2015), less is known about how the sectoral allocation of

capital came about. It is therefore also unclear whether the developments

in the first decade of EMU were an unfortunate one-off or something that

could have been foreseen and possibly prevented.

In this chapter, we first document empirically how the growth of the

nontradable sector in Southern Europe was a broad-based phenomenon ex-

tending beyond the construction- and real estate sectors. We then proceed by

constructing a tractable two-sector two-region general equilibrium model of

a monetary union. We simulate the non-linear transition path following the

permanent drop in the real interest rate experienced by Southern Europe in

the run-up to the introduction of the euro. The fall in the interest rate in-

duces a regional demand boom, which increases demand for both tradable

and nontradable goods. Whereas the nontradable sector is able to increase

prices and output, the tradable sector faces foreign competition and thus

has less room to increase prices. Therefore, in real terms, capital and labor

are cheaper in the nontradable sector and are (re)allocated to this sector.

In the North, Southern demand for tradables and upward pressure on the

EMU-wide interest rate induce wage moderation and a shift of resources to

the tradable sector. As such, cost competitiveness positions in the North and

the South diverge, while Southern external debt accumulates. Absent a debt-

elastic interest rate or a debt limit, there is nothing to stop this process. When

we extend the model to include a third region—the ‘Rest of the World’—the

effects of monetary integration in the Southern part of the union are ampli-

fied, while spillovers to the North are more muted, in part due to an appre-

ciation of the union’s exchange rate that limits the growth of the Northern

tradable sector.

We validate the model predictions empirically using a reduced form

Bayesian panel-VAR for 10 euro area countries. The key predictions hold

up well: countries which experienced negative interest rate shocks (relat-

ive to the euro area average), experienced faster growth of the nontradable

sector, but not faster growth of the tradable sector. As such, also empirically,


Sectoral allocation and macroeconomic imbalances in EMU 167

negative interest rate shocks lead to growth of the relative size of the nontra-

dable sector. Negative interest rate shocks also contribute to a deteriorating

current account balance.

This chapter contributes to an emerging body of research that studies

the allocation of incoming capital flows in Southern Europe, both across

and within sectors, and the effects thereof on the external position and pro-

ductivity.3 Most closely related, Benigno and Fornaro (2014), Piton (2015)

and Kalantzis (2015), show that in a small open economy framework an

exogenous fall in the interest rate leads to (relative) growth of the nontra-

dable sector. Piton (2015) suggests that higher mark-ups in the nontradable

sector contribute to the relative growth of this sector, while Benigno and

Fornaro (2014) show how—in a setting where only the tradable sector ex-

periences productivity growth—the reallocation of labor to the nontradable

sector contributes to stagnating productivity growth. Kalantzis (2015) em-

phasizes how the interest rate drop results in both growth of the nontrad-

able sector as well as increasing leverage, which together make balance-of-

payments crises more likely.

The focus of this literature on small open economies models implies that

any feedback effects that might occur in a monetary union are omitted.4 We

show these feedback effects to be relevant, contributing to both wage mod-

eration and a shift of resources towards the tradable sector in North. In this

way, we also complement studies by Gadatsch et al. (2016) and Bettendorf

and Leon-Ledesma (2015), who focus on domestic drivers of the German

3 Reis (2013) focuses on financial frictions to show why relatively unproductive firms in thenontradable sector grow at the expense of the tradable sector. Gopinath et al. (2017) and Cec-chetti and Kharroubi (2015) show that financial frictions can contribute to the misallocationof capital within sectors, as capital is allocated to firms that have higher net worth but are notnecessarily more productive. Sy (2016) emphasizes how the interaction of a common mon-etary policy and heterogeneous inflation rates implies real rates that are lower in the Souththan in the North, contributing to growth of the Southern nontrable sector. To rationalize theboom-bust cycle experienced by much of the Eurozone, Ozhan (2017) shows how bank bal-ance sheets can amplify fluctuations that are driven by news on the valuation of non-tradedsector capital.

4 Over 1999-2007, the former high interest rate countries’ represented 32-36% of euro areaGDP and 40-41% of the euro area population, rendering the assumption that these countriescan be represented as small open economies within the euro area counterfactual. See alsoFagan and Gaspar (2007).


168 Chapter 5

current account surplus.

Moreover, while our model remains relatively tractable otherwise, we

allow for monopolistic competition and differences in productivity levels

between regions and sectors. This set-up allows us to show that the realloc-

ation towards the nontradable sector that follows the interest rate shock is

qualitatively invariant to the degree of competition in the nontradable sec-

tor and to differences in productivity levels across sectors. Thus, the realloc-

ation of resources also follows through when the nontradable sector is the

less competitive and/or less productive one. Accordingly, our results offer a

structural explanation for the empirical findings documented by Borio et al.

(2016) and Cette et al. (2016), that credit booms like those experienced by

Southern Europe after the introduction of the euro are associated with a

productivity slowdown driven by a reallocation of resources towards less

productive sectors.

The results in this chapter raise important policy issues, as to correct-

ing external imbalances and preventing new ones. The model suggests that

many of the developments in the first decade of EMU should not have come

as a surprise. Indeed, our model suggests that growth of the Southern non-

tradable sector, deteriorating competitiveness, and current account deficits

are all relatively straightforward consequences of the economic boom in-

duced by the sharp decline in real interest rates. A sufficiently strong reac-

tion of Southern interest rates to the accumulating debt, a leaning-against-

the-wind type of fiscal policy, or possibly macroprudential measures, could

have helped to moderate these developments, preventing the need for a

sharp rebalancing process later on.

In the absence of timely stabilizing measures, investors ‘waking up’ and

demanding a higher interest rate premium induces a sharp rebalancing pro-

cess during which Southern GDP falls. We investigate various policy op-

tions that can accommodate a less disruptive rebalancing process, focusing

on product market reforms that have the potential to both boost growth

and facilitate the rebalancing process. Firstly, we analyze the effects of a lib-

eralization of the Southern nontradable sector, i.e., allowing for more do-



mestic competition. Perhaps counter-intuitively, but in line with Cavelaars

(2006), this does not improve the region’s external position. As mark-ups

in the nontradable sector come down, demand for nontradable goods in-

creases and the sector expands. Total output in the South grows, while the

external position marginally deteriorates. Spillovers from liberalizing the

Northern nontradable sector are limited. Secondly, we simulate a decrease in

the mark-up on tradable goods (interpreted as a deepening of the European

internal market). This induces a shift of productive resources towards the

tradable sector and boosts growth, although in the short run it does come at

the expense of a deterioration of the external position of the union as whole.

The rest of the Chapter is organized as follows. Section 5.2 documents

stylized facts. Section 5.3 presents the model. Section 5.4 shows the simula-

tion results and Section 5.5 shows the empirical results. Section 5.6 discusses

policy option and Section 5.7 concludes.

5.2 Stylized facts

In anticipation of the introduction of the euro, nominal interest rates in

Southern Europe fell sharply. As this partly reflected falling inflation ex-

pectations, the drop of economically more relevant real interest rates was

less extreme. Nevertheless, the drop was substantial: in the three years prior

to the introduction of the euro, real one-year yields—the nominal one-year

yield on government debt minus Consensus inflation expectations one-year

hence—in Italy, Ireland, Portugal and Spain (the ‘IIPS’, with data for Greece

being unavailable before 1998) fell by on average four percentage points, see

Figure 5.1 panel a. Over the same period, real rates in the rest of the euro

area (REA) remained roughly constant.

In the first years of EMU, interest rates in the entire euro area increased.

Following the collapse of the dotcom bubble, interest rates came down again.

However, inflation expectations and realized inflation in the GIIPS remained

persistently above those in the REA. Consequently, real rates in the GIIPS re-

mained below those in the REA up to the onset of the crisis.


170 Chapter 5

Figure 5.1. Interest rates and macroeconomic imbalances

-300

-200

-100

0

100

200

300

400

1998 2000 2002 2004 2006

d: Current account (billion $)

100

120

140

160

180

200

1998 2000 2002 2004 2006

c: Export (1998 = 100)

-2

-1

0

1

2

3

4

5

1996 1998 2000 2001 2004 2006

a. Real interest rates (1y gov. bonds)

IIPS GIIPS REA

100

110

120

130

140

150

160

170

180

1998 2000 2002 2004 2006

b: Domestic demand (1998 = 100)

Notes: The IIPS include Ireland, Italy, Portugal and Spain, the GIIPS also includes Greece.The REA includes the other EMU-12 countries: Austria, Belgium, Finland, France, Germany,Luxembourg and the Netherlands. Figure 1 panel a shows the real 1 year interest rate, cal-culated as the 1 year yield on government bonds minus inflation expectations over the same1 year period (calculated using Consensus data). Figures 1 panels b and d are based on datafrom the IMF WEO database October 2015, figure 1c uses AMECO data.

Low and falling interest rates induced a domestic demand boom in the

GIIPS (Figure 5.1 panel b). Over 1999-2007, domestic demand in the GIIPS

grew by on average 3% a year. In the REA, domestic demand increased by

1.7% a year. The demand boom in the GIIPS contributed to a surge in im-

ports, but was not matched by a similar increase in exports. Export perform-

ance even somewhat lagged behind the REA (Figure 5.1 panel c). As a result,

the current account of the GIIPS which was balanced at the onset of EMU,

deteriorated sharply in the years thereafter. The GIIPS’ current account defi-

cit was matched by an increasing current account surplus in the REA (Figure



5.1 panel d).5 Accordingly, the external position of the euro area as a whole

remained close to balance.

In Figure 5.2 we plot value added in the nontradable sector to show that

growth was mostly concentrated in the nontradable sector. To this end, we

use data from the World Input Ouput Database (Timmer et al., 2015) and

estimate for each sector in each country the share of production that is ab-

sorbed domestically. We aggregate these results for all euro area countries,

weighing each member by its share in total euro area output. Subsequently,

we construct the nontradable sector by selecting those sectors that depend

most heavily on domestic demand. Figure 5.A.1 in the Appendix shows for

the year 1999 per sector the share of production that is absorbed domestic-

ally. In Figure 5.2 panels a and b, we construct the nontradable sector by ag-

gregating the 8 sectors that depend most heavily on domestic demand and

which jointly produce 33% of total euro area output. In Figure 5.2 panels

c and d, we construct the nontradable sector by aggregating the 14 sectors

that depend most heavily on domestic demand and which jointly produce

50% of total output.

Figure 5.2 panel a and c show the growth of the nontradable and trade-

able sector. Irrespective of the threshold used, the nontradable sector in the

GIIPS realized higher growth rates than the nontradable sector in the REA.

This growth differential could be the result of higher GDP growth rates in

the GIIPS, i.e., higher growth in both the nontradable and tradable sectors,

potentially reflecting catch-up growth. However, Figure 5.2 panel b and d

show that this is not the dominant factor. Value added in the nontradable

sector as percentage of GDP grows in the GIIPS countries, while it decreases

in the REA. Hence, these latter countries realized predominantly export led

growth, while in the GIIPS the nontradable sector grew faster than the trad-

able sector.

Numerous country or sector specific reasons can be identified to explain

the allocation of capital inflows. One popular explanation focuses on exces-

5 Consistent with this pattern, Berger and Nitsch (2014) provide evidence of a significantwidening of bilateral intra-euro area trade imbalances.


172 Chapter 5

Figure 5.2. Nontradable sector growth and as percentage of GDP

a: Value added nontradable sector (33% of output) b: Value added nontradable sector as percentage of GDP

(33% of output)

c: Value added nontradable sector (50% of output) d: Value added nontradable sector as percentage of GDP

(50% of output)

e: Value added nontradable sector without construction f: Value added nontradable sector as percentage of GDP

(33% of output) without construction (33% of output)

Notes: GIIPS contain Greece, Ireland, Italy, Portugal, Spain. The REA contains the other EMU-12 countries excluding

Luxembourgh: Austria, Belgium, Finland, France, Germany and the Netherlands. In Figure a, c, e 1999 = 100.

80

100

120

140

160

180

200

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

21.0%

21.2%

21.4%

21.6%

21.8%

22.0%

22.2%

22.4%

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

29.0%

29.5%

30.0%

30.5%

31.0%

31.5%

1999 2000 2001 2002 2003 2004 2005 2006 2007 200880

100

120

140

160

180

200

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

80

100

120

140

160

180

200

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

14.5%

15.0%

15.5%

16.0%

16.5%

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

GIIPS REA

Notes: The GIIPS include Greece, Ireland, Italy, Portugal and Spain. The REA includes theother EMU-12 countries excluding Luxembourgh: Austria, Belgium, Finland, France, Ger-many and the Netherlands. In panels a, c and e 1999 = 100. Source: own calculations basedon WIOD, release 2013 (Timmer et al., 2015), see Appendix 5.A.



sive growth in the real estate sector. Housing bubbles have certainly been

an important factor driving current account imbalances in countries such

as Spain and Ireland. However, the nontradable boom was not limited to

real estate and construction. Figure 5.2 panels e and f show the growth rate

and share of GDP of value added in the nontradable sector excluding the

construction and real estate sector. Although growth rates are a bit lower

than in Figure 5.2 panel a, the overall pattern is the same. Thus, the rapid

growth of the nontradable sector appears to have been more broad-based

than is sometimes suggested.6

5.3 The model

The model builds on the two-region two-sector framework introduced by

Stockman and Tesar (1995) and Obstfeld and Rogoff (1995). The regions are

labeled ‘North’ and ‘South’. Following monetary integration, both regions

become part of a single monetary union. Both regions exist of a large number

of identical households, a large number of firms and a government which all

have perfect foresight. The union has a single central bank which keeps the

union price level constant. Households consume, supply labor, accumulate

financial assets (one-period risk free bonds), hold money, and own the firms.

Firms buy capital from capital producers and hire labor from households.

In each region there are two types of firms, producing nontradable goods

(N) and tradable goods (T) respectively. The tradable good is used either as

consumption good or as investment in the tradable and nontradable capital

stock. The nontradable good can only be consumed.

The monetary union as a whole is a closed economy, a simplifying as-

sumption which we relax in Section 5.4.2. Within the union labor is mo-

bile across sectors, but not between regions. Exchange rates are fixed, i.e.,

pegged in the immediate run-up to EMU, and irrevocably fixed thereafter.

In the run-up to EMU, regional interest rates are higher in South than in

6 The financial sector, another sector typically mentioned as a fast growing (closed) ‘services’sector, is too open to be part of our nontradable sector and thus not driving the growththereof.


174 Chapter 5

North by an exogenous premium, which can be thought of as reflecting

e.g. exchange rate or inflation risk (for a similar approach, see Kollmann

et al., 2015). Following the introduction of the euro and the establishment of

a single central bank, this premium disappears and interest rates converge.

5.3.1 Households

Households that live in region j ∈ n, s, where n = North and s = South,

maximize lifetime utility by choosing consumption, labor supply and money

holdings:

U j =∞

∑v=0

(βj)v

[log Cj

t −θ(Lj

t)1+σl

1 + σl

], (5.1)

θ, σl > 0 and 0 < βj < 1,

where Cjt denotes consumption in region j at time t and Lj

t denotes labor

supply. The parameters βj = 1/(1 + ρj), θ and σl denote the discount rate,

the weight of labor in the utility function and the inverse of the elasticity of

work effort, respectively.

The consumption good is a composite of a nontradable Cj,Nt and a trad-

able good Cj,Tt which are transformed into the final consumption good via

a standard aggregator function: Cjt =

(Cj,N

t

)η (Cj,T

t

)1−ηwhere 0 < η < 1

denotes the share of nontradables. Note that the tradable good is either pro-

duced in the home region j or in the foreign region denoted by j′, i.e. con-

sumption of the tradable good in region j is denoted as Cj,Tt = Cjj,T

t + Cjj′,Tt .

The nontradable good is only produced domestically. The consumer price

index is a composite of the price of the nontradable good Pj,Nt and the price

of the tradable good Pj,Tt and is obtained by minimizing the expenditure ne-

cessary to obtain one unit of the composite good Cjt , i.e., minimizing Pj

t Cjt =

∑jj′P

j′,Tt Cjj′,T

t + Cj,Nt Pj,N

t subject to the constraint Cjt = (Cj,N

t )η(Cj,Tt )1−η :

Pjt =

(Pj,N

t

)η (Pj,T

t

)1−η

(η)η (1− η)1−η. (5.2)



For the tradable good the law of one price holds, as there are no trade re-

strictions any price difference is arbitraged away: Pn,Tt = Ps,T

t .

Households can borrow or lend via single period bonds issued in both

North and South. We assume that, prior to EMU, there is an exogenous

wedge between Southern and Northern risk-free interest rates:

r f ,nt + ω = r f ,s

t , (5.3)

where r f ,jt is the endogenously determined risk free interest rate on bonds

issued by region j and ω is an exogenous premium that disappears after

monetary integration. The uncovered interest rate parity condition ensures

that after integration the nominal interest rate is the same in both regions:

r f ,nt = r f ,s

t ≡ r f ,et , where r f ,e

t is the union interest rate.7

It is a characteristic of international business cycle models with incom-

plete financial markets that there is no unique deterministic steady state, see

e.g. Schmitt-Grohe and Uribe (2003) and Boileau and Normandin (2008). In

particular, whereas the interest rate pins down both regions’ net lending,

their external asset holdings are indeterminate. To pin down the equilibria,

and prevent any one region from endlessly accumulating debt, we introduce

a debt-elastic interest rate premium xjt. The interest rate premium increases

in the regions’ external debt level:

xjt = ξe−N j

t − 1, (5.4)

where ξ denotes how strongly the interest rate premium responds to debt

accumulation and N jt ≡ NFAj

t/(Pj,Tt Y j,T

t + Pj,Nt Y j,N

t ) denotes the net foreign

asset position as percentage of GDP, NFAjt denotes the net financial assets

of region j and Pj,Tt Y j,T

t and Pj,Nt Y j,N

t denote nominal GDP in the tradable

and nontradable sector respectively. As such, a region’s borrowing rate is

given by rjt = r f ,j

t + xjt. This implies that the rate paid by the borrower is

7 As the union-wide price level is kept constant by the monetary authority, at the union levelthe nominal interest rate equals the real interest rate. This is not necessarily the case at thelevel of the individual regions however, as movements in relative prices can drive a wedgebetween nominal and real rates.


176 Chapter 5

higher than the one received by the lender. The difference can be thought of,

and microfounded as, the cost of financial intermediation (Boileau and Nor-

mandin, 2008). Alternatively, it can be interpreted as a premium on default

risk that is absorbed by the intermediary bearing the risk.8

The household budget constraints are represented by:9

j′

∑ Bj′ jt + Pj,T

t Cj,Tt + Pj,N

t Cj,Nt =

j′

∑(

1 + rjt−1

)Bj′ j

t−1 + πj,Nt + π

j,Tt + Lj

tWjt ,

(5.5)

where LjtW

jt denotes nominal labor income, Bj′ j

t denotes net bonds issued in

country j and held by households in country in j′, πj,Nt and π

j,Tt are firm

profits (hence households are the true owners of the firms). Households

maximize their utility by choosing consumption and labor supply and bond

holdings, subject to the budget constrained and a no-Ponzi condition. Labor

is perfectly mobile within regions, but does not move across the two re-

gions. As a consequence, the wage rate is equal across sectors but may differ

between regions.

5.3.2 Firms

In both regions the economy is occupied by two types of intermediate firms

which produce wholesale tradables (T) and wholesale nontradables (N), re-

spectively. For brevity we define Z ∈ (T, N). Intermediate firms hire labor

from the household sector, buy capital from the capital producers, and sell

their wholesale goods to retailers. Retailers use the wholesale goods to pro-

duce the final goods. The retailers are introduced only to realize monopol-

istic competition in a tractable manner.

8 During the first decade of EMU risk premia were mostly absent while they suddenlyspiked when the solvency of the Southern states became questionable. In Section 5.4.3 wediscuss the consequences of a sudden increase in the interest rate premium.

9 We assume that, within regions, actuarially fair priced state-contingent securities exist thatinsure each household against idiosyncratic variations in labor and dividend income. Con-sequently, at the regional level, individual household income will correspond to aggregatehousehold income.



The aggregate production technologies of the nontradable and tradable

intermediate firms are specified by a Cobb-Douglas form:

yj,Zt (i) = Aj,Z

t

(K j,Z

t−1(i))1−αZ (

Lj,Zt (i)

)αZ

, (5.6)

where Aj,Zt denotes the productivity level in region j and sector Z, K j,Z

t de-

notes the physical capital stock and αZ denotes the share of labor in produc-

tion. Total labor demand is given by Ljt = Lj,N

t + Lj,Tt . Both types of firms

accumulate capital according to the following accumulation identities:

K j,Zt+1 = (1− δ)K j,Z

t + I j,Zt , (5.7)

where I j,Zt denotes investment in the physical capital stock and δ is the de-

preciation rate. The nontradable and tradable intermediate firms minimize

their costs subject to their production constraint, see Appendix 5.B.

Capital producers sell their capital to the intermediate firms in a per-

fectly competitive environment. For reasons of tractability we assume that

capital producers acquire investment (mobile across borders and between

sectors) to produce capital. They borrow from the domestic households to

produce capital. Consequently, the return to capital equals the domestic

borrowing rate rjt. The nontradable and tradable capital production func-

tion is subject to diminishing returns to scale and represented by: I j,Zt −

φPj,Tt

2

(I j,Zt

K j,Zt− δ

)2

K j,Zt , where capital adjustment costs are denoted in the price

of tradables. Maximizing profits yields the price of capital, see Appendix

5.B.

We model monopolistic competition by introducing a retail sector that

aggregates the intermediate goods produced by the nontradable and trad-

able firms respectively, into two (tradable and nontradable) final goods. Re-

tailers buy the products of the intermediate firms and use the following CES

production functions to produce the final goods (Dixit and Stiglitz, 1977):

Y j,Zt =

[∫ 1

0yj,Z

t (i)1−1/µj,Zdi]1/(1−1/µj,Z)

, (5.8)


178 Chapter 5

where yj,Zt (i) denotes nontradable or tradable output produced by interme-

diate nontradable or tradable firm i, Y j,Zt is the final goods and µj,Z denotes

the degree of substitutability between the intermediate products and de-

termines the amount of market power of the nontradable and tradable firms.

In the limit (µj,Z → ∞), pricing is perfectly competitive. Hence, both the

nontradable and tradable sector intermediate firms face downward sloping

demand (5.8) for their products because we assume imperfect substitutabil-

ity between intermediate products.

Retailers minimize the cost of buying output from intermediate firms∫ 10 Pj,Z

t (i)Y j,Zt (i)di subject to the CES production function (5.8). The retail

sector is perfectly competitive. Therefore both type of retail firms maximize

their profit function by setting prices equal to their marginal costs mct(i).

The aggregate price of nontradable and tradable products can be expressed

as the weighted sum of the intermediate good prices:

Pj,Zt =

[∫ 1

0pj,Z

t (i)1−µj,Zdi]1/1−µj,Z

, (5.9)

where pj,Zt (i) is the price set by intermediate firm i for intermediate input

yj,Zt (i).

5.3.3 Monetary authority and government sector

As prices are flexible, monetary policy cannot affect the real allocation of re-

sources. However, nominal variables, in our case the nominal price level,

are affected by monetary policy and are indeterminate without a policy

rule. Given our monetary union set-up, we assume therefore that the monet-

ary authority stabilizes the union-wide price level Pet , which consists of the

weighted sum of the aggregate price levels of the two regions:

Pet = hPn

t + (1− h)Pst , (5.10)

where h denotes the respective share of North and (1− h) denotes the share

of South in the Union. As such, the aggregate price levels within the two re-



gions, as well as the price level of nontradable- and tradable products within

the regions, are allowed to fluctuate.

The government engages in debt-financed government consumption.

The government uses both tradable and nontradable goods to produce ag-

gregate government consumption Gjt . The aggregator function is similar to

the aggregator function for the private consumption good, and uses equal

weights:

Gjt =

(Gj,N

t

)η (Gj,T

t

)1−η, 0 < η < 1. (5.11)

The government minimizes the cost of a given amount of government con-

sumption: Pjt Gj

t = ∑jj′P

j′,Tt Gjj′,T

t + Gj,Nt Pj,N

t . It takes the prices of the trad-

able and nontradable goods as given. Accordingly, government consump-

tion of both goods depends on the respective prices levels of both goods.

While we set steady state government spending equal to zero, we do exper-

iment with debt-financed government spending (or saving) shocks.

5.3.4 Market equilibrium conditions

The goods market equilibrium in the market for nontradables requires that

production of nontradable goods in each region is equal to consumption of

nontradable goods of consumers and the government in each region:

Y j,Nt = Cj,N

t + Gj,Nt , (5.12)

where Gj,Nt denotes government spending in the nontradable sector. The

market for tradable goods and investment is fully internationally integrated.

Hence, equilibrium requires that in the Union as a whole production is equal

to consumption and investment:

∑j

Y j,Tt = ∑

j

[Cj,T

t + I j,Tt + I j,N

t + ACjt + ICj

t + Gj,Tt

]. (5.13)


180 Chapter 5

Here, ACjt = ∑Z

[φPj,T

t2

(I j,Zt

K j,Zt− δ

)2

K j,Zt

]denotes the combined capital ad-

justment costs in the tradable- and the nontradable sector (which, like the

investment good itself, is expressed in terms of tradables) and ICjt denotes

the cost of financial intermediation (xjtNFAj

t). While the current account of

the union as a whole thus needs to be balanced, individual regions are al-

lowed to run deficits or surpluses. As borrowing and lending is only pos-

sible through one-period risk free bonds, a region’s net financial asset posi-

tion (NFAt) is denoted by:

NFAjt =

(1 + r f ,j

t−1

)NFAj

t−1+

Pj,Tt

(Y j,T

t − Cj,Tt − I j,T

t − I j,Nt − ACj

t − ICjt − Gj,T

t

). (5.14)

The current account balance is defined as the first difference of a country’s

NFAt. Finally, equilibrium in the market for financial assets requires:

NFAnt + NFAs

t = 0. (5.15)

5.3.5 Calibration

We calibrate the model to match the evolution of the Northern and South-

ern parts of the euro area following monetary integration, and to simulate

the effect of various policy measures. Time is quarterly. The parameter val-

ues are presented in Table 5.1. Both regions are equal in size. For simplicity,

productivity levels are equal across regions and sectors, an assumption we

relax later on. We furthermore assume that the discount factor in the North

is higher than in the South. This assumption ensures that prior to monet-

ary integration, both the South and the North run close to balanced current

accounts. Following monetary integration and the resulting convergence of

interest rates, the South borrows from the North. We calibrate the size of

the country specific debt-elastic risk premium such that the South’s external

debt stabilizes at 70% of GDP, in line with the average external debt of the

GIIPS in 2007. There are two important differences between the tradable





βn Discount factor households, North 0.990βs Discount factor households, South 0.980σl Inverse of the elasticity of work effort 2.000θ Weight of leisure 1.000η Share of nontradables in consumption 0.667αT Share of labor in the tradable production function 0.550αN Share of labor in the nontradable production function 0.600δ Depreciation rate of physical capital 0.030µn,N Market power nontradable sector, North 5.000µs,N Market power nontradable sector, South 3.500µj,T Market power tradable sector, region j 10.000ξ Credit premium reaction 0.007Aj,Z Productivity region j, sector Z 1.000h Relative share of North in union 0.500φ Capital adjustment costs 2.000

and nontradable sector and between the nontradable firms in Northern and

Southern Europe which are introduced to mimic the stylized facts but have

no effect on the general results. First, we assume that αN > αT, i.e., the non-

tradable sector is more labor intensive than the tradable sector. Second, we

assume that µn,N > µs,N , i.e., the nontradable sector in the Southern part of

Europe is less competitive than the nontradable sector in the Northern part

of Europe. Third, in our baseline calibration the tradable sector is equally

competitive in both parts of the union (due to the existence of a single mar-

ket) and more competitive than the nontradable sector (that is, µj,T > µj,T∀j).

As we analyze a large and highly persistent (arguably permanent) shock

that can lead to large and long-lasting deviations from the initial steady

state, log-linearizing the model around the steady state can lead to mislead-

ing results. Instead, we carry out a numerical simulation of the full nonlinear

model, using Dynare’s deterministic setting (see Adjemian et al., 2011). This

assumes that i) the shock to interest rates is unexpected and ii) agents are


182 Chapter 5

certain that no future shocks will occur (‘perfect foresight’). The key advant-

age of this approach is that it provides us with the exact transition path of

the endogenous variables following the shock to the Southern interest rate,

whereas any log-linearized solution becomes less accurate the further the

variables move away from their initial steady state.

5.4 Model simulations

5.4.1 Two-region model

After monetary integration, the interest premium paid by South disappears

and interest rates in North and South converge, see Figure 5.3 panel a. South

experiences a demand boom: households reduce saving and increase con-

sumption (Figure 5.3b), while firms increase investment. Capital starts to

flow from North to South.

The capital inflow needs to be allocated between the tradable and non-

tradable sector. The allocation depends on two main channels. First, as wages

increase (Figure 5.3c), the more labor intensive nontradable sector experi-

ences a relative cost increase compared to the tradable sector. The relative

price of the nontradable good thus increases. As a result, demand for non-

tradable products increases less than the demand for tradable products (‘de-

mand effect’). Southern consumption of tradables increases by more than

the consumption of nontradables.

However, whereas tradable goods can be imported, nontradable goods

need to be produced at home. Consequently, a second channel emerges

which more than offsets the first one. In the absence of foreign competition,

firms in the nontradable sector have relatively ample space to increase prices

when their production costs increase without slackening demand (‘supply

effect’). Competition with the North implies that Southern firms active in the

tradable sector have less room to increase their prices as production costs in-

crease. The rising relative price of nontradables implies that, in real terms,

capital and labor are cheaper inputs in the nontradable sector. The effect is



Figure 5.3. Consequences of monetary integration

1.0%

1.5%

2.0%

2.5%

1 3 5 7 9 11 13 15

a: risk-free quarterly interest rate

RF (S) RF (N)

2.84

2.86

2.88

2.90

2.92

1.56

1.58

1.60

1.62

1.64

1 3 5 7 9 11 13 15

b: consumption

C (S) C (N r-axis)

1.32

1.33

1.34

1.35

1.36

1.12

1.13

1.14

1.15

1.16

1 3 5 7 9 11 13 15

c: wage developments

Wage (S) Wage (N r-axis)

0.84

0.86

0.88

0.90

0.92

0.94

0.73

0.74

0.75

0.76

1 3 5 7 9 11 13 15

d: sectoral allocation (North)

KN/KT (N) LN/LT (N r-axis)

0.98

1.00

1.02

1.04

1.06

1.08

0.79

0.80

0.81

0.82

1 3 5 7 9 11 13 15

e: sectoral allocation (South)

KN/KT (S) LN/LT (S r-axis)

0.65

0.66

0.67

0.68

0.69

0.70

0.74

0.75

0.76

0.77

0.78

0.79

1 3 5 7 9 11 13 15

f: relative sectoral size

YN/YT (S) YN/YT (N r-axis)

1.06

1.07

1.08

1.09

1.10

1.11

1 3 5 7 9 11 13 15

g: real exchange rate

Real exchange rate (P_S / P_N)

-10%

-8%

-6%

-4%

-2%

0%

-60%

-50%

-40%

-30%

-20%

-10%

0%

1 3 5 7 9 11 13 15

h: external position (% GDP)

NFA (S) CA (S r-axis)

1.0%

1.5%

2.0%

2.5%

1 3 5 7 9 11 13 15

i: risk-adjusted quarterly interest

rate

R (S) R (N)

Notes: The Figure shows the effects of the permanent elimination of the wedge ω betweenSouthern and Northern risk-free interest rates in Equation (5.3). The x-axis displays the num-ber of quarters following the shock.


184 Chapter 5

a reallocation of capital and labor towards the nontradable sector (Figure

5.3f).

In the North the opposite effect occurs: Southern demand for capital in-

creases interest rates, which causes households to increase savings. Whereas

Southern demand for tradables grows, domestic demand in the North falls.

As a result, the nontradable sector shrinks and both wages and the relative

price of nontradables fall. Capital and labor are reallocated to the growing

tradable sector.

The Southern boom in consumption and investment and the shift of pro-

ductive resources to the nontradable sector cause the external position of

South to deteriorate (Figure 5.3h). The increase in external debt causes an

increase in the risk premium until the interest rate reaches a level at which

the capital inflow stops and the net foreign asset position stabilizes. The

rising interest rate also facilitates a shift of resources back to the tradable

sector to produce the goods necessary to balance imports and exports.

All results are obtained under the assumption of equal productivity levels

across sectors and countries. This simplifies the interpretation of the results

(e.g. ensuring that a sectoral reallocation of resources does not itself affect

GDP), but is clearly not a realistic assumption. We therefore calibrate the

productivity levels in the tradable and nontradable sector in both regions

using the database constructed by Mano and Castillo (2015). Productivity

is calculated as total value added per sector and country divided by total

hours worked in each sector and country. Mano and Castillo (2015) classify

a sector as tradable if more than 10% of the sector is exported. We aggreg-

ate productivity at the region level by taking the weighted average based

on the countries share in total EMU valued added. The resulting productiv-

ity levels, where we normalize tradable productivity in the North to 1 are:

AN,n = 0.76, AT,n = 1, AN,s = 0.79, AT,s = 0.92.

Qualitatively, the results are unchanged: the reallocation to the nontra-

dable sector following monetary integration still follows through when the

nontradable sector is the less productive sector (results not included but

available on request). As such, even if productivity in both sectors would



Figure 5.4. Consequences of monetary integration: effects of including theRoW

1.0%

1.5%

2.0%

2.5%

1 3 5 7 9 11 13 15

a: risk-free quarterly interest

rate (South)

RF RF

-80%

-60%

-40%

-20%

0%

-14%

-10%

-6%

-2%

2%

1 3 5 7 9 11 13 15

b: external position (South, %

GDP)

CA CA

NFA r-axis NFA r-axis

0.94

0.95

0.96

0.97

1 3 5 7 9 11 13 15

c: exchange rate RoW / EA

Exchange rate RoW/EA

1.50

1.52

1.54

1.56

1.58

1.60

1 3 5 7 9 11 13 15

d: relative prices (South)

PN/PT PN/PT

0.95

1.00

1.05

1.10

0.79

0.80

0.81

0.82

1 3 5 7 9 11 13 15

d: sectoral allocation (South)

KN/KT KN/KT

LN/LT r-axis LN/LT r-axis

0.80

0.85

0.90

0.95

0.73

0.74

0.75

0.76

1 3 5 7 9 11 13 15

f: sectoral allocation (North)

KN/KT KN/KT

LN/LT r-axis LN/LT r-axis

Notes: The Figure shows the effects of the permanent elimination of the wedge ω betweenSouthern and Northern risk-free interest rates in Equation (5.3) in a closed (2-region)- andopen (3-region) version of the model.

remain constant, the relative growth of the nontradable sector hurts aggreg-

ate productivity. Accordingly, the model offers a structural explanation for

the empirical findings documented by Borio et al. (2016) who show that

credit booms like those experienced by Southern Europe after the introduc-

tion of the EMU are associated with a productivity slowdown driven by a

reallocation of resources towards less productive sectors.

Results do also not depend qualitatively on the degree of competition in

the Southern nontradable sector (see Figure 5.D.2 in Appendix 5.D). Even

with a perfectly competitive nontradable sector, the fall in Southern interest

rates induces a reallocation towards the nontradable sector. As such, elimin-

ating ‘rent seeking’ does—in our setting at least—not prevent the allocation

of incoming capital flows towards the production of nontradables.


186 Chapter 5

5.4.2 Including the Rest of the World

So far, we assumed a closed economy for the monetary union as a whole.

In this section, this simplifying assumption is relaxed by including a third

country labeled ‘Rest of the World’ (RoW). The size of the labor force of

RoW is equal to the combined Northern and Southern part of the monet-

ary union. RoW has a flexible exchange rate with the monetary union, is

connected to (initially, the Northern part of) the monetary union via an un-

covered interest rate parity condition and the Law of One Price and in terms

of parameters mimics the Northern part of the monetary union. It is, there-

fore, best thought of as another advanced economy. See Appendix 5.C for

the technical details.

As before, we simulate an interest rate shock in South, see Figure 5.4.

The addition of a third region somewhat amplifies the effects of this shock

in South, while it attenuates the effects in North. Two channels are at work.

First, there is an exchange rate effect. The Southern boom increases the union-

wide risk-free rate and induces an appreciation of the union’s currency. To

remain competitive, prices of tradeable products must fall. In South, this

amplifies the relative price increase of the nontradable good which contrib-

utes to an even faster reallocation of resources towards the nontradable sec-

tor. In North, this mitigates the fall in the relative price of the nontradable

good, which dampens the reallocation towards the tradable sector. Secondly,

and somewhat trivially, the addition of a third region increases the size of

the total economy. Southern imports no longer need to come exclusively

from North. As a result, the impact of the Southern boom on interest rates

in North is attenuated. Interest rates do rise, and North continues to realize

a current account surplus, but this is only approximately half as large as in

the two-region case. In contrast, the attenuated response of risk-free interest

rates implies South enjoys a boom and a current account deficit which are

even larger than in the two-region case.

The Southern boom also induces the RoW to run a current account sur-

plus. Whereas the surplus in the Northern part of the union was induced

by a rising interest rate, the RoW surplus is induced by the appreciation of



the union currency. RoW tradable goods get cheaper which means by the

Law of One Price that the domestic currency price increases. Consequently,

resources are reallocated to the tradable sector, the RoW enjoys a moderate

boom and realizes a surplus on its current account.

5.4.3 Crisis

Our model is primarily constructed, and calibrated, to examine how mon-

etary integration affects the external position and sectoral allocation of re-

sources in Southern Europe. Due to the presence of a debt-elastic interest

rate, the model is stable. Yet, even in this setting, it is fairly straightforward

to see how a crisis could occur. As in e.g. Eggertsson and Krugman (2012),

the crisis can be modeled as a ‘Minsky moment’ in which risk aversion sud-

denly increases. In our case, this is easiest to simulate through an unexpec-

ted, permanent increase in the elasticity of the risk premium to a region’s

debt level (see (5.4) in Section 5.3). The effects thereof are mostly intuitive

and the opposite of the ones presented in Section 5.1: external borrowing

and investment in the South collapse, consumption falls, and resources tem-

porarily reallocate to the tradable sector. Eventually a new steady state, with

a lower external debt level and a stable current account, is reached. Figure

5.D.3 in Appendix 5.D presents the results in more detail.

5.5 Empirical analysis

5.5.1 Methodology and data

In this chapter we motivate our model by the sharp decline in real interest

rate experienced by Southern Europe in the run-up to the introduction of

the euro. However, the predictions of our model are more general and can

be summarized as follows: a negative interest rate shock, e.g. as experienced

by multiple Southern European countries in anticipation of EMU, leads to a

reallocation of resources towards the nontradable sector and the emergence

of a current account deficit. The opposite holds for a positive interest rate


188 Chapter 5

shock.

In order to verify this prediction empirically, we estimate a standard

macroeconomic framework with output growth, inflation and a short-term

interest rate which is often used to identify interest rate shocks (see, e.g.,

Svensson 1997 and Clarida et al. 1999). We, however, allow for three devi-

ations to fit the estimation more closely to our theoretical model. First, we

split output growth in nontradeable and tradeable output growth to exam-

ine separately the effect of an interest rate shock on the growth rates of each

sector. Second, as our model is formulated in real terms, we estimate the

model in real terms. Third, we add current account flows, thereby opening

up the model, as we are interested in the effect of interest rate shocks on

cross-border capital flows.

We estimate the following reduced form Bayesian panel-VAR system:

Xt =α0 + α1Dt + Φ(L)Xt + εt, (5.16)

where Φ(L) ≡ Φ1L1 + ... + ΦpLp is a lag polynomial and Xt is a vector

containing the observed variables as discussed:

Xt =

[(yN

t,i − yNt ), (y

Tt,i − yT

t ),(

Bt,i

Yt,i− Bt

Yt

), (ir

t,i − irt)

]′, (5.17)

where yNt,i denotes the growth rate of the nontradable sector at time t in coun-

try i from which we subtract the average growth rate of the nontradable

sector in the euro area, yNt , to control for any EA-wide trend, yT

t,i denotes the

growth rate of the tradable sector of which we subtract the average growth

rate of the tradable sector in the euro area, yTt , ir

t,i is the ex-ante expected real

interest rate of which we subtract the average real interest rate in the euro

area irt .

10 Finally, Bt,i/Yt,i denotes a country’s current account balance as per-

10 The use of time-fixed effects also controls for common trends at the euro area level, but inthat case the control group is a non-weighted average of developments in individual coun-tries. This places a disproportional weight on developments in small countries, and doesnot give an accurate picture of EA-wide developments. We experimented with time-fixedeffects by including annual dummy variables to our specification. Results are qualitativelythe same, see Figure 5.D.4 in Appendix 5.D.



centage of GDP of which we subtract the euro area average current account

balance Bt/Yt.11

If applicable we include an exogenous dummy variable denoted by the

vector of dummies Dt ≡[

D f ct , Dec

t

]′. The dummy D f c

t controls for the global

financial crisis taking the value 1 in 2008 and 2009 and zero otherwise and

the dummy Dect controls for the euro area crisis taking the value 1 in 2011

and 2012 and zero otherwise. Finally, εt is a vector of stacked reduced form

residuals.

To identify the shocks we assume that the structural shocks are ortho-

gonal and use a Cholesky decomposition. The ordering is as specified in

(5.17), i.e, we let the real interest rate adjust contemporaneously to nontra-

dable and tradable growth shocks, but growth in the nontradable and trad-

able sector is affected by a real interest rate shock only with a lag. The model

is estimated using a (pooled) Bayesian estimation procedure. The data is

observed at an annual frequency and therefore only one lag is included.

In order to let the data speak as much as possible, we impose a (agnostic)

Minnesota prior: all lag coefficients takes a prior value of 0.8. The hyper-

parameters are set at standard values, i.e., the overall tightness parameter is

set equal to 0.1 and the lag decay parameter is set equal to 1. As (5.16) also

includes two exogenous dummy variables we set the exogenous parameter

tightness to 100.

The growth rates for both the nontradeable and tradeable sector are cal-

culated using Eurostat data for countries for which disaggregated output

time series are available: Austria, Belgium, Germany, Finland, France, Italy,

Ireland, Netherlands, Spain and Portugal. The disaggregated output time

series are available on an annual basis and categorized in either the trad-

able or nontradable sector. Similar to the stylized facts presented in Figure

5.2 panel c and d, we construct the nontradable sector by aggregating the

14 sectors that depend most heavily on domestic demand and which jointly

11 All variables are expressed in growth rates or percentages and subsequently demeaned.These transformations ensure that our data series are stationary. Stationarity is also con-firmed by the Levin et al. (2002) panel unit root test.


190 Chapter 5

produce 50% of total output.12 Figure 5.A.1 in the Appendix shows which

sectors are classified as a nontradable sector. We use annual nominal in-

terest rates on 1-year government bonds as a proxy for the country-wide

nominal interest rate and the Consensus forecast inflation expectations one

year ahead to transform the nominal interest rates into ex-ante real interest

rates.13 Finally, we use data from the World Economic Outlook database to

collect data on current account balances.

The time series cover the period 1996-2013 as no disaggregated data is

available for all countries for the years 2014 and 2015. As in general no data

is available for Luxembourg, we drop this country from our sample. For

Greece we lack data on nominal interest rates on one-year governments

bonds before 1999. As our inflation expectations measure covers inflation

expectations over a one-year period, the only consistent way to create ex-

ante real interest rates is to use one-year interest rates. Table 5.D.3 in the

Appendix summarizes the descriptive statistics.14

Preferably we would like to estimate the full model using the identific-

ation restrictions as presented in Section 5.3, see, e.g., Smets and Wouters

(2003) and Christiano et al. (2005) for two seminal contributions to DSGE

estimation. However, given the limited availability of disaggregated output

data at the sectoral level, we resort to panel data and use a reduced form

estimation approach.

12 The Eurostat classification is slightly different from the WIOD classification presented inFigure 5.2. Specifically, the WIOD contains more detailed information about the opennessof the sectors, but data is only available until 2011. We therefore match the WIOD classi-fication with the Eurostat classification to categorize the Eurostat sectors in a tradable andnontradable sector, see Table 5.A.1 in the Appendix.13 We also estimated the model with both nominal interest rates and inflation expectations.Results, which are not presented here for conciseness, are qualitatively the same.14 For robustness we experiment with 10-year government bond yields as those are alsoavailable for Greece before 1999. The nominal rates are transformed in ex-ante expected realrates using the one-year inflation expectations. To do so we assume that inflation expect-ations remain constant over the 10-year period. Results, which are not presented here, arelargely consistent with the results presented below.



5.5.2 Empirical results

We estimate the Bayesian panel-VAR over the sub-period 1996-2008 and

over the entire sample period 1996-2013.15 The first regression covers the

build-up of euro area imbalances as explained by our model where the

second regression also includes the bust as simulated in Section 5.4.3. As

dynamics may differ between the build-up phase and the sudden bust, it is

informative to estimate the Bayesian panel-VAR over both the sub-period

and the entire period.

Figure 5.5 shows the impulse response functions following a positive

interest rate shock for the period 1996− 2008. In line with the model predic-

tions, a country that is hit by a positive interest rate shock of one standard

deviation experiences a decline in the growth rate of the nontradable sector.

Figure 5.5 shows that the same does not hold for the tradable sector. For one,

the impulse response function is smaller in magnitude, but more import-

antly, countries are less probable to experience any change in the growth

rate of the tradable sector as the credibility interval includes zero. However,

in contrast to the predictions of the model, a country’s current account is not

likely to be affected by an exogenous increase in the real interest rate.

As the model is symmetric we can also interpret negative interest rate

shocks, as experienced in Southern Europe. A back-of-the-envelope calcu-

lation shows that the 4 percent point (unconditional) decrease in Southern

European interest rates relative to Northern European interest rates (see Fig-

ure 5.1), caused, according to the impulse response functions, a relative in-

crease in nontradeable growth of about 1− 2% per annum for a period of

6− 8 years. Thereafter the impulse response function is slowly decreasing to

zero. This increase comes on top of the overall trend of increasing nontrade-

able sector growth observed in all European countries. Hence, it appears

that interest rate shocks can explain a large fraction of the higher growth

rates of the Southern European nontradeable sector described in Figure 5.2.

Figure 5.6 shows the results for the period 1996− 2013, which also in-

15 The Bayesian panel-VAR is estimated using the ECB BEAR-toolbox developed by Dieppeet al. (2016), which builds on the methodology surveyed by Canova and Ciccarelli (2013).


192 Chapter 5

Figure 5.5. Real interest rate shock for sample period 1996-2008

5 10 15 20

-0.3

-0.2

-0.1

0

5 10 15 20

-0.2

-0.1

0

5 10 15 20

0

0.2

0.4

Res

pons

e of

:

Shock:

5 10 15 20

-0.1

0

0.1

0.2

Notes: The black lines represent the median response to a real interest rate shock estimatedover the time period 1996-2008. Shaded areas denote 68% credibility intervals which are gen-erated by drawing 50, 000 draws from the posterior distribution of which 40, 000 draws arediscarded as burn-in iterations. Horizontal axes specify years. Vertical axes denote percentpoint deviations from average euro area growth, ratio or rate.

cludes the bust period. The response of nontradable and tradable sector

growth rates to an interest rate shock is now more markedly divergent.

A positive interest rate shock still causes the nontradable sector growth to

slow. However, the effect of the interest rate shock on tradable sector growth

is positive and at longer horizons marginally different from zero at the 68%

credibility interval. These results are in line with the model which predicts

a small increase in the growth rate of the tradeable sector following a posit-

ive interest rate shock. They also help explain part of the strong growth of

Northern Europe’s tradeable sector.

In the bust phase, a positive real interest rate shock also has a positive

impact on the current account balance. A rising interest rate relative to the

euro area average is associated with a sharply improving current account



Figure 5.6. Real interest rate shock for sample period 1996-2013

5 10 15 20

-0.2

-0.1

0

5 10 15 20

-0.1

0

0.1

0.2

5 10 15 20

0

0.2

0.4

5 10 15 20-0.2

0

0.2

0.4

0.6

0.8

Res

pons

e of

:

Shock:


balance, in line with a ’sudden stop’ pattern.

5.6 Policy options and discussion

The results presented highlight major challenges in terms of correcting ex-

isting imbalances and preventing new ones. Macroprudential policy limit-

ing private sector borrowing could play an important role in preventing the

developments stressed in this chapter from reoccuring. Fiscal policy also

offers a fairly straightforward tool to lean against excessive private borrow-

ing. Fiscal consolidation curtailing domestic demand directly improves the


194 Chapter 5

external position.16 The fall in domestic demand also reduces the relative

price of nontradables, inducing a shift of productive resources towards the

tradable sector.

Currently, however, the first challenge for EMU is to reduce existing im-

balances in a way that does not unduly harm GDP growth. In Section 5.4.3

we showed that a sudden increase in the interest rate premium induces

a sharp rebalancing process as we saw in practice. In this section various

policy options that can accommodate a less disruptive rebalancing process

are examined.

5.6.1 Increasing competition in the nontradable sector

Figure 5.7 shows the effects of a liberalization of the nontradable sector in

South, i.e., a decrease in the mark-up on nontradable products. A liberal-

ization of the nontradable sector causes prices of nontradeable products

to fall, increasing relative demand for nontradables. Real income also in-

creases, contributing to increased demand for both tradable and nontrad-

able products. As nontradable products need to be produced at home, this

leads to an expansion of the nontradable sector. The domestic shortage of

tradable products is imported from the North. Overall, output and the relat-

ive size of the nontradable sector increase while the current account position

deteriorates.

Spillovers from a liberalization of the Northern nontradable sector are

limited. The North grows and from a Southern perspective both external

demand and the interest rate increase. GDP and the sectoral allocation of re-

sources in the South are largely unaffected. The Northern reforms do induce

a fall in the Northern price level, which—given that prices at the union level

are held constant by the single central bank—temporarily allows for some

inflation in the South. This improves the ratio of net financial assets to GDP.

Figure 5.D.5 in Appendix 5.D displays the results in more detail.

16 In a monetary union, even away from the zero lower bound, Ricardian equivalence breaksdown due to the fact that there is only a limited reaction of the union-wide interest rateto fiscal policy in an individual country/region. As such, private borrowing does not fullyoffset government savings, and the external position improves.



Figure 5.7. Product market reform in South, transition path

1.82

1.83

1.84

1.85

1.86

1.55

1.56

1.57

1.58

1.59

1 3 5 7 9 11 13 15

b: private consumption

C (S) C (N r-axis)

1.37

1.42

1.47

1.52

1 3 5 7 9 11 13 15

a: relative price of nontradables

PN/PT (S) PN/ PT (N)

0.69

0.71

0.73

0.75

0.77

1 3 5 7 9 11 13 15

d: relative sectoral size

YN/YT (S) YN/YT (N)

5.04

5.06

5.08

5.10

5.12

4.06

4.08

4.10

4.12

4.14

1 3 5 7 9 11 13 15

c: GDP

GDP (S) GDP (N, r-axis)

-0.3%

-0.2%

-0.1%

0.0%

0.1%

-72%

-71%

-70%

1 3 5 7 9 11 13 15

f: external position (% GDP)


0.94

0.96

0.98

1

0.76

0.78

0.8

0.82

1 3 5 7 9 11 13 15

e: sectoral allocation

KN/KT (S) LN/LT (S r-axis)

Notes: This Figure shows the effects of a permanent 10 percentage points reduction of mark-ups in the Southern nontradable sector. Simulation conducted using the 2-region version ofthe model; results using the 3-region version are highly similar and available upon request.

5.6.2 Deepening the internal market

The introduction of the euro was intended in part to deepen the internal

market, thereby increasing competition in the market for tradables. Evid-

ence on whether the euro achieved this is mixed. Deepening the internal

market is however still seen as a policy priority, see e.g. European Com-

mission (2015). We simulate the effects of a deepening of the internal market

through a decrease in the mark-up on tradables in both regions of the EA. As

shown in Figure 5.8, this induces a fall in the relative price of tradables and

thereby speeds up the desired shift of resources towards the tradable sector.

It boosts investment and GDP growth. As demand for tradable goods in-

creases faster than supply, the EA initially develops a trade deficit with the

RoW. This is accommodated by an appreciation of the euro, which allows


196 Chapter 5

Figure 5.8. Deepening the EA internal market, transition path

1.32

1.34

1.36

1.38

1.40

1.42

1.44

1.46

1.50

1.55

1.60

1.65

1 3 5 7 9 11 13 15


PN/PT (S) PN/ PT (S r-axis)

0.60

0.62

0.64

0.66

0.68

0.70

0.72

1 3 5 7 9 11 13 15


YN/YT (S) YN/ YT (N)

1.80

1.81

1.82

1.83

1.84

1.53

1.54

1.55

1.56

1.57

1 3 5 7 9 11 13 15


C (S) C (N r-axis)

-2.0%

-1.5%

-1.0%

-0.5%

0.0%

0.5%

-90%

-86%

-82%

-78%

1 3 5 7 9 11 13 15

e: external position South (%

GDP)


5.10

5.15

5.20

5.25

5.30

4.04

4.08

4.12

4.16

4.20

4.24

1 3 5 7 9 11 13 15

c: GDP

GDP (S) GDP (N, r-axis)

0.92

0.94

0.96

0.98

1 3 5 7 9 11 13 15 17 19

f: exchange rate RoW / EA

Exchange rate RoW/EA

Notes: This Figure shows the effects of a permanent reduction of mark-ups in the Northernand Southern tradable sector.

for a rise in the price of tradable goods in the RoW that dampens local de-

mand. Over the long run, the tradable sector in the RoW shrinks marginally,

whereas the tradable sector in both regions of the EA grows significantly.

5.7 Conclusion

In this chapter, we documented empirically how growth of the nontradable

sector in Southern Europe was a broad-based phenomenon that extended

beyond the construction- and real estate sectors. We then showed in a two-

region two-sector general equilibrium model that many of the key character-

istics of the first decade of EMU can be explained by the major interest rate

shock the Southern European countries experienced when joining EMU. The

interest rate shock can be shown to explain both the divergence of current

account positions and wage rates between Northern and Southern Europe,



as well as the allocation of capital and labor towards the nontradable sector

in South. The allocation of incoming capital to the nontradable sector occurs

irrespective of any differences in competitiveness or productivity across sec-

tors or regions. We confirmed the relation between interest rate shocks and

growth of the nontradable sector in a Bayesian panel-VAR for 10 euro area

countries over the period 1996− 2013.

Our results highlight several challenges for policy makers. When for-

eign borrowing is not matched by an increased export capacity, a point

made forcefully by Giavazzi and Spaventa (2010), solvability problems can

emerge. In our model a debt-elastic interest rate prevents these solvabil-

ity problems from occurring. In reality, the reaction of interest rates to the

external debt level was arguably absent. Fiscal policy would have offered

a fairly straightforward tool to lean against excessive private borrowing.

When imposed after the collapse of the boom, increased public savings can

still help speed up the reallocation of productive resources towards the trad-

able sector, but only at the cost of an even deeper recession. In a quest for

a more desirable solution, we investigated two options for product market

reform. Improving the European internal market for tradables, i.e., further

strengthening competition in this sector, appears to be the most promising

option, facilitating a further rebalancing towards tradables while simultan-

eously boosting growth.

Our findings suggest various directions for further research. Through-

out this chapter, we have assumed that goods are either tradable or non-

tradable. From a policy perspective, it is a highly relevant question to what

extent improving the European internal market for services can contribute

to increasing the share of traded ‘goods’, and what effects this would have.

Additionally, our study focuses on the sectoral allocation of capital inflows

in a nearly frictionless environment. Others have focused on the allocation

of capital within sectors, highlighting the role of financial frictions. Combin-

ing both perspectives seems a fruitful avenue for further research. Finally,

our study points to the need of explicitly monitoring a country’s foreign bor-

rowing, which is done via the Macroeconomic Imbalances Procedure (MIP)


198 Chapter 5

since 2011. To enforce the MIP, instruments are needed to curtail excessive

borrowing. Macroprudential policy offers promise in this respect, but still

faces major challenges that need further investigation.

5.A Sectoral dependence on domestic demand

Figure 5.A.1. Share of value added from domestic demand in the euro area

0 0.2 0.4 0.6 0.8 1

Water Transport

Chemicals and Chemical Products

Basic Metals and Fabricated MetalRubber and Plastics

Air TransportElectrical and Optical Equipment

Mining and QuarryingPulp, Paper, Paper , Printing and Publishing

Wood and Products of Wood and Cork

Other Non-Metallic MineralOther Supporting and Auxiliary Transport Activities; Activities of…

Transport EquipmentCoke, Refined Petroleum and Nuclear Fuel

Textiles and Textile ProductsMachinery, Nec

Renting of M&Eq and Other Business Activities

Inland TransportFinancial Intermediation

Leather, Leather and FootwearWholesale Trade and Commission Trade, Except of Motor Vehicles and…

Post and Telecommunications

Agriculture, Hunting, Forestry and FishingElectricity, Gas and Water Supply

Manufacturing, Nec; RecyclingRetail Trade, Except of Motor Vehicles and Motorcycles; Repair of…

Sale, Maintenance and Repair of Motor Vehicles and Motorcycles;…Other Community, Social and Personal Services

Food, Beverages and Tobacco

Hotels and RestaurantsReal Estate Activities

ConstructionEducation

Public Admin and Defence; Compulsory Social SecurityHealth and Social Work

Private Households with Employed Persons

Notes: The red-bar sectors sum to a nontradable sector that produces 33% of total euro areaoutput and the red- and yellow-bar sectors sum to a nontradable sector that produces 50%of total euro area output. Source: own calculations using WIOD, release 2013 (Timmer et al.,2015).



Table 5.A.1. Classification

WIOD Classification VA Dom- Total Cumulative EUROSTATestically output share & KLEMS

codes

Private Households with Employed Persons 100.0% 26194 0.2% THealth and Social Work 99.8% 574381 4.7% QEducation 99.7% 378891 7.7% PReal Estate Activities 99.7% 890490 14.6% LPublic Admin and Defence; 99.5% 603584 19.4% O

Compulsory Social SecuritySale, Maintenance and Repair of Motor 99.0% 223209 21.1% G45 - G46 -

Vehicles and Motorcycles - G47Construction 98.6% 913288 28.3% FHotels and Restaurants 98.5% 359423 31.1% IRetail Trade, Except of Motor Vehicles and 98.1% 485831 34.9% G47

Motorcycles; Repair of Household Goods

Other Community, Social and Personal Serv. 97.2% 429865 38.2% R + S + UElectricity, Gas and Water Supply 97.0% 271372 40.4% DPost and Telecommunications 94.2% 255341 42.4% J - J62-63

+ H53Wholesale Trade and Commission Trade, 92.6% 643040 47.4% G46

except of motor vehicles and motorcyclesFinancial Intermediation 92.4% 614538 52.2% K

Inland Transport 90.6% 292791 54.5% H - H53Renting of M&Eq and Other 90.4% 1144176 63.5% M + N

Business Activities + J 62-63Other Supporting and Auxiliary Transport 85.5% 238207 65.3% H - H53

Activities; Activities of Travel AgenciesAgriculture, Hunting, Forestry and Fishing 84.0% 315989 67.8% AMining and Quarrying 83.2% 76820 68.4% BWood and Products of Wood and Cork 79.8% 80283 69.0% CFood, Beverages and Tobacco 77.1% 568989 73.5% COther Non-Metallic Mineral 76.5% 151818 74.7% CPulp, Paper, Printing and Publishing 74.4% 285858 76.9% CCoke, Refined Petroleum and Nuclear Fuel 73.6% 127712 77.9% CBasic Metals and Fabricated Metal 68.7% 475078 81.6% CManufacturing, Nec; Recycling 66.3% 138993 82.7% CRubber and Plastics 62.9% 152780 83.9% CAir Transport 60.5% 74950 84.5% H - H53Textiles and Textile Products 54.3% 183217 85.9% CLeather, Leather and Footwear 52.7% 46897 86.3% CMachinery, Nec 46.9% 366348 89.2% CElectrical and Optical Equipment 44.5% 416984 92.4% CTransport Equipment 42.7% 533056 96.6% CChemicals and Chemical Products 40.8% 391655 99.7% CWater Transport 26.7% 40050 100.0% H - H53


200 Chapter 5

5.B Model solution

Households

Household maximization problem:

max∞

∑v=0

(βj)v

log (Cj,Nt )η(Cj,T

t )1−η − θ(Ljt)

1+σl

1 + σl+

χ(

mjt

)1−σm

1− σm

s.t.

j′

∑j

Bjt + Pj,T

t Cj,Tt + Pj,N

t Cj,Nt + Mj

t =j′

∑j(1 + rj

t−1)Bjt−1+

πj,Nt + π

j,Tt + Lj

tWjt + Mj

t−1. (5.B.1)

Households maximize their utility by choosing both consumption goods,

labor supply, money holding and bond holdings, subject to the budget con-

straint and a no-Ponzi condition. The FOCs are:

1− η

Cj,Tt

= Pj,Tt λh

t , (5.B.2)

η

Cj,Nt

= Pj,Nt λh

t , (5.B.3)

λht = λh

t+1(1 + rjt)βj, (5.B.4)

θ(Ljt)

σl = W jt λh

t , (5.B.5)

χ(

mjt

)−σm= λh

t − λht+1βj, (5.B.6)

where λht denotes the households’ Lagrangian multiplier. Using the FOC

for the tradable consumption good (5.B.2), Cj,Tt , to substitute the Lagrangian

multiplier out gives:

Pj,Tt Cj,T

t =Pj,T

t+1Cj,Tt+1

(1 + rjt)βj

, (5.B.7)

1− η

Cj,Tt Pj,T

t

=η

Cj,Nt Pj,N

t

, (5.B.8)



Cj,Tt Pj,T

t =1− η

θ

W jt

(Ljt)

σl, (5.B.9)

Mjt

Pjt

=

[χ

Cj,Tt Pj,T

t1− η

(1 + rj

t

rjt

)] 1σm

. (5.B.10)

Firms

Retailers are perfectly competitive and therefore we consider a representat-

ive retailer which buys input yj,Zt (i) from intermediate firm i and produces

output Y j,Zt according the following aggregator function:

Y j,Zt =

[∫ 1

0yj,Z

t (i)(µj,Z−1)/µj,Z

di]µj,Z/(µj,Z−1)

, (5.B.11)

and has a budget constraint which is denoted by: Pj,Zt Y j,Z

t =∫ 1

0 pj,Zt (i)yj,Z

t (i)di.

Retailers minimize their cost subject to their production function:

Ljt =

∫ 1

0pj,Z

t (i)yj,Zt (i)di−

λrt

(Y j,Z

t −[∫ 1

0yj,Z

t (i)(µj,Z−1)/µj,Z

di]µj,Z/(µj,Z−1)

), (5.B.12)

where λrt is the retailers marginal cost of producing an extra unit of final

output. The FOC w.r.t. to production input yj,Zt (i) of firm i and production

input yj,Zt (i′) of firm i′ and dividing these FOCs gives the relative pricing

equation:

yj,Zt (i) = yj,Z

t (i′)

(pj,Z

t (i)

pj,Zt (i′)

)−µj,Z

. (5.B.13)

If we combine the budget identity Pj,Zt Y j,Z

t =∫ 1

0 pj,Zt (i)yj,Z

t (i)di and aggreg-

ator function (5.B.11) and substitute subsequently the relative pricing equa-


202 Chapter 5

tion (5.B.13) to solve for Pj,Zt , we obtain:

Pj,Zt =

[∫ 1

0pj,Z

t (i)1−µj,Zdi]1/1−µj,Z

. (5.B.14)

We can substitute (5.B.14), together with the relative pricing equation (5.B.13)

for yj,Zt (i), back in the budget identity to obtain retailer demand for interme-

diate product yj,Zt (i):

yj,Zt (i) =

[Pj,Z

t

pj,Zt (i)

]µj,Z

Y j,Zt . (5.B.15)

Intermediary firms minimize their costs which consists of unit labor costs,

the opportunity costs of holding a unit of capital and the costs of buying

capital from the capital producers. The intermediate firm Lagrangian is ex-

pressed by:

Lj,Zt (i) =W j

t Lj,Zt (i) + (1 + rj

t)qj,Zt K j,Z

t (i)− qj,Zt (1− δj)K j,N

t (i)

− λj,Zt (i)

(Aj,Z

t (K j,Zt (i))1−αj

(Lj,Zt (i))αj

), (5.B.16)

where λj,Zt (i) is the Lagrangian multiplier of the firms which represents the

intermediate firms’ marginal costs. The FOC w.r.t. Lj,Zt (i) is represented by:

W jt = λ

j,Zt (i)

αjyj,Zt (i)

Lj,Zt (i)

, (5.B.17)

where yj,Zt (i) = Aj,Z

t (K j,Zt (i))1−αj

(Lj,Zt (i))αj

. The FOC w.r.t. K j,Zt (i) is repres-

ented by:

1 + rjt =

λj,Zt (i) (1−αj)yj,Z

t (i)K j,Z

t (i)+ (1− δ)qj,Z

t−1

qj,Zt

. (5.B.18)

Using both FOCs in the production function gives the expression for mar-



ginal costs, λj,Zt , which is the same for all intermediate firms:

λj,Zt =

1

Aj,Zt

((1 + rj

t)qj,Zt + (1− δ)qj,Z

t−1

(1− αj)

)(1−αj)(W j

tαj

)αj

. (5.B.19)

Capital producers are perfectly competitive. Consequently, the individual

capital producer’s optimization problem corresponds to the aggregate prob-

lem. The aggregate capital stock evolves according to:

K j,Zt+1 = (1− δj)K j,Z

t + I j,Zt . (5.B.20)

Capital producers combine new investment I j,Zt with undepreciated cap-

ital to produce new capital according to the following production function:

Φ(

I j,Zt

K j,Zt

)K j,Z

t = I j,Zt −

φPj,Tt

2

(I j,Zt

K j,Zt− δ

)2

K j,Zt . This functional form ensures

that the price of capital is equal to unity in steady state. Capital producers

choose investment I j,Zt to maximize the profits from producing capital and

then sell their capital for a price qj,Zt :

maxI j,Zt

qj,Z

t

[I j,Zt −

φPj,Tt

2

(I j,Zt

K j,Zt

− δ

)2

K j,Zt

]− Pj,T

t I j,Zt

. (5.B.21)

The FOC gives the price of capital:

qj,Zt = Pj,T

t

[1 + φ

(I j,Zt

K j,Zt

− δ

)]. (5.B.22)

As retailers face imperfect substitutability between intermediate inputs, in-

termediate firms have some market power and can set their prices as a mark

up over their marginal costs λj,Zt . Intermediary firms maximize their profits

w.r.t. prices:

πj,Zt (i) = [pj,Z

t (i)− λj,Zt (i)]yj,Z

t (i), (5.B.23)

The FOC w.r.t. pj,Zt (i) after we have substituted demand for yj,Z

t (i) (5.B.15)


204 Chapter 5

and solving for pj,Zt (i) gives:

pj,Zt (i) =

(µj,Z

µj,Z − 1

)λ

j,Zt . (5.B.24)

Hence, intermediate firms set prices as a mark-up over their marginal costs.

We can subsequently use (5.B.11) and (5.B.14) to aggregate over all firms

and rewrite (5.B.17), (5.B.18) and (5.6) in terms of aggregate output Y j,Zt and

aggregate prices Pj,Zt .

Government sector

The aggregator function for the public consumption good is similar to the

aggregator function for the private consumption good, with equal weights:

Gjt = (Gj,N

t )η(Gj,Tt )1−η , 0 < η < 1. (5.B.25)

The government minimizes the cost of a given amount of government con-

sumption: Pjt Gj

t = ∑jj′P

j′,Tt Gjj′,T

t + Gj,Nt Pj,N

t . It takes the prices of the trad-

able and nontradable goods as given. Accordingly, government consump-

tion of both goods depends on the respective prices levels of both goods:

Gj,Tt

Gj,Nt

=

(1− η

η

)Pj,N

t

Pj,Tt

. (5.B.26)

5.C Including the Rest of the World

The RoW economy is set up the same way as the Northern and Southern re-

gion, but has its own (floating) exchange rate. As before, the various regions

are denoted by superscript j, with j ∈ n, s, r.Prior to monetary integration, we assume the Rest of the World to be

connected to the Northern part of the euro area via an UIP:

1 + rnf ,t = (1 + rr

f ,t)Er,n

t+1

Er,nt

, (5.C.27)



Table 5.C.2. Calibrated parameters in RoW


βr Discount factor households 0.990θr Weight of leisure 0.200ηr Share of nontradables in consumption 0.667µr Market power nontradable sector 5.000ξr Credit premium reaction 0.007AN,r Productivity 1.000AT,r Productivity 1.000

where Er,nt is the nominal exchange rate between the Rest of the World and

the Northern part of the euro area (expressed as the price of one unit of RoW

currency in units of region n currency). As in the 2-region version of the

model, Northern and Southern currencies are pegged, with the UIP between

North and South given by:

rnf ,t + ω = rs

f ,t. (5.C.28)

As such, in the above setup Southern Europe pays a risk premium vis-a-

vis both the Northern part of Europe and the rest of the world that can be

easiest thought of as an exchange rate risk premium. Following monetary

integration, as the peg is exchanged for a more-difficult-to-reverse common

currency, this premium disappears.

The Law of One Price is assumed to hold both within Europe, as between

Europe and the rest of the world:

pnt = Er,n

t prt . (5.C.29)

World equilibrium in the market for financial assets is now given by:

NFAnt + NFAs

t + Er,nt NFAr

t = 0, (5.C.30)

where NFAjt represents the net financial assets held by region j denominated


206 Chapter 5

in domestic currency.

Table 5.C.2 lists the RoW calibrated parameters. We set the weight of leis-

ure to 0.2 in RoW, so that the GDP and labor force in the rest of the world

equals that of the combined Northern and Southern European region. In

terms of other parameters, such as the degree of competition in the nontra-

dable sector, the Rest of the World mimics the Northern part of Europe. It is,

thus, best thought as another advanced economy (e.g. the US).

5.D Robustness checks

Figure 5.D.2. Impact of monetary integration on relative sectoral sizes inSouth, for different values of the nontradeable markup in South

0.70

0.74

0.78

0.82

0.86

0.90

1 3 5 7 9 11 13 15

μ = 3.5 μ = 5 μ = 6.5

Notes: The Figure illustrates the effects of monetary integration on the relative sectoral size

in South, Ys,Nt

Ys,Tt

, for different values of µs,N , in the 2-region version of the model. See Section

5.4.



Figure 5.D.3. Reaction to a sudden increase in the elasticity of interest ratesto debt levels

0.87

0.89

0.91

0.93

0.95

0.97

0.74

0.75

0.76

0.77

1 3 5 7 9 11 13 15

d: sectoral allocation (North)

KN/KT LN/LS (r-axis)

-2%

0%

2%

4%

6%

8%

10%

12%

14%

-90%

-80%

-70%

-60%

-50%

-40%

-30%

-20%

-10%

0%

1 3 5 7 9 11 13 15

g: external position south (% GDP)

NFA CA (r-axis)

0.5%

1.0%

1.5%

1 3 5 7 9 11 13 15

a: risk-free quarterly interest rate

RF South RF North

1.82

1.84

1.86

1.88

1.50

1.52

1.54

1.56

1 3 5 7 9 11 13 15

b: consumption

C South C North (r-axis)

1.35

1.36

1.37

1.38

1.39

1.10

1.11

1.12

1.13

1.14

1 3 5 7 9 11 13 15

c: wage developments

W South W North (r-axis)

1.03

1.04

1.05

1.06

1.07

1 3 5 7 9 11 13 15

f: real exchange rate

Real exchange rate (PS/PN)

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

1 3 5 7 9 11 13 15

h: risk-adjusted quarterly interest

rate

R South R North

0.96

0.97

0.98

0.99

1 3 5 7 9 11 13 15

i: exchange rate RoW/ EA

Exchange rate RoW/ EA

0.85

0.87

0.89

0.91

0.93

0.95

0.75

0.76

0.77

0.78

1 3 5 7 9 11 13 15


KN/KT LN/LS (r-axis)

Notes: The Figure illustrates the effects of a permanent increase in the debt-elasticity of in-terest rates. Simulations are conducted using the 3-region version of the model. Startingpoint of the simulations is the post-monetary integration steady state.


208 Chapter 5

Table 5.D.3. Descriptive statistics

yNt,i − yN

t yTt,i − yT

tBt,iYt,i− Bt

Ytirt,i − ir

t yNt,i yT

t,iBt,iYt,i

irt,i

Mean 0.48 0.47 −1.29 0.44 3.90 3.72 1.40 1.66Median 0.37 0.25 −0.91 −0.08 3.89 4.77 0.99 1.19Std. Dev. 2.87 3.83 5.00 5.11 3.45 5.99 1.23 5.14Observations 198 198 198 198 198 198 198 198

Figure 5.D.4. Real interest rate shock for sample period 1996-2013 (time fixedeffects)

5 10 15 20-0.3

-0.2

-0.1

0

0.1yNt;i ! 7y

Nt

5 10 15 20

-0.1

0

0.1

0.2

0.3yTt;i ! 7y

Tt

5 10 15 20

0

0.2

0.4

Bt;i

Yt;i!

7Bt7Yt

5 10 15 20-0.2

00.20.40.60.8

irt;i !7irt

Res

pons

e of

:

Shock:




Figure 5.D.5. Product market reform in North, transition path

1.25

1.27

1.29

1.31

1.33

1.35

1.37

1.39

1.45

1.50

1.55

1.60

1 3 5 7 9 11 13 15


PN/PT (S) PN/PT (N) r-axis

1.84

1.85

1.86

1.87

1.55

1.56

1.57

1.58

1 3 5 7 9 11 13 15


C (S) C (N) r-axis

0.67

0.69

0.71

0.73

0.75

1 3 5 7 9 11 13 15


YN/YT (S) YN/ YT (N)

0.945

0.947

0.949

0.770

0.775

0.780

1 3 5 7 9 11 13 15


KN/KT LN/LT r-axis

5.08

5.10

5.12

5.14

5.16

5.18

4.04

4.06

4.08

4.10

4.12

4.14

1 3 5 7 9 11 13 15

c: GDP

GDP (S) GDP (N) r-axis

-0.5%

0.0%

0.5%

-71%

-70%

-69%

1 3 5 7 9 11 13 15

f: external position South (% GDP)

NFA CA r-axis

Notes: The Figure shows the effects of a permanent reduction of mark-ups in the NorthernNT sector. Simulations conducted using the 2-region version of the model. Simulations startfrom the post-monetary integration steady state.


Chapter 6

Conclusion

6.1 Summary

In this thesis we focused on the macroeconomic consequences and determ-

inants of fluctuations in credit supply. The global financial crisis reminded

us of the importance of credit in determining macroeconomic fluctuations.

The abrupt decline in available credit put a hold on economic activity while

the build-up of financial imbalances that eventually led to the bust star-

ted with credit being structurally miss-allocated. The mainstream macroe-

conomic models could not inform policymakers how to respond to deterior-

ating lending conditions in credit markets and how to prevent the build-up

of imbalances in the future. In this thesis we tried to fill part of this gap by

analyzing factors that affect the availability and allocation of credit supply.

In Chapter 2 we analyzed the impact of credit default risk on bank lend-

ing and in Chapter 3 we extended this analysis by incorporating the im-

pact of credit default losses. These chapters showed that if credit default

losses are higher than anticipated, i.e., loan loss provisioning is insufficient

to cover credit default losses, credit supply declines which puts a break on

economic activity, mainly via investment. In Chapter 2 we showed, for mon-

etary policy to be effective, it is paramount that banks are well-capitalized.

If banks do not have sufficient bank capital to cover credit default losses

and cannot or will not issue new bank equity, monetary transmission is im-


212 Chapter 6

peded. Although the central bank lowers the policy rate in response to the

decline in economic activity, the lending rate is disconnected from the policy

rate because banks are constrained by their leverage ratio. Consequently

lending rates remain high and credit supply falls.

In Chapters 4 and 5 we examined the role of credit allocation in the build-

up of imbalances that could, once winded down, adversely impact bank

capitalization and deteriorate credit supply. Credit should be allocated ef-

ficiently and productively to prevent the build-up of imbalances. In these

chapters we showed, however, that when credit supply increases, credit

tends to flow to sectors that produce goods that are both nontradable and

have a low supply elasticity. These characteristics are typically associated

with the real estate sector. Albeit, Chapter 5 argues explicitly that the build-

up of imbalances in southern Europe went beyond the real estate and con-

struction sector and could best be classified as a nontradeable sector boom.

Chapter 4 also shows how growth of the market for mortgage loans (i.e.

credit that flows to the real estate sector) might be related to growth of the

unregulated shadow banking sector. On itself, strong growth of the shadow

banking sector has no adverse consequences for financial or economic sta-

bility. However, the creation of more uninsured shadow bank deposits in-

creases liquidity risk which is not fully reflected in market prices because the

shadow banking sector implicitly relies on liquidity support by the central

bank. Shadow banks issue, as a consequence, too many uninsured deposits

compared to socially optimal amounts.

In Chapter 5 we showed that especially the nontradeable sector grows

after a negative interest rate shock as the one experienced by Southern Eu-

rope in the run-up to the EMU. The negative interest rate shock can also

explain the divergence of current account positions and wage rates between

Northern and Southern Europe. We confirmed this relation between negat-

ive interest rate shocks and growth of the nontradeable sector in a Bayesian

panel-VAR for 10 euro area countries.


Conclusion 213

6.2 Policy implications

The results in this thesis highlight several challenges for future policy de-

cisions. In Chapters 2 and 3 we highlight that banks must be sufficiently

well-capitalized to guarantee effective monetary transmission. Accumulat-

ing sufficient capital buffers during a boom, e.g., via timely loan loss provi-

sioning, countercyclical capital buffers and/or retained earnings, improves

monetary transmission during a slump. If capital buffers turn out to be in-

sufficient and banks are reluctant to issue new bank equity, the central bank

can stimulate retained earnings by decreasing the policy rate. Rebuilding

bank capital via retained earnings is, however, slow and lengthens the per-

sistence of shocks. In this case, a swift bank recapitalization via, e.g., a bail-

in or a mandatory equity issuance can restore monetary transmission while

these measures also overcome the looming costs of moral hazard.

In Chapters 4 and 5 we investigate various policy measures that could

prevent the build-up of imbalances and shift the allocation of resources to

more productive sectors. The results emphasize the salient role for micro-

and macroprudential policy tools and structural reforms to safeguard an

efficient allocation of credit. Chapter 4 examines tighter loan-to-value con-

straints for mortgage loans and shows how these constraints can facilitate

a reallocation of credit to corporate lending and attenuate fluctuations in

house prices and the supply of mortgage loans.

In Chapter 4 we argue that the central bank can address the external-

ity associated with the creation of uninsured shadow bank deposits. Central

banks can realign private and social interests by paying interest on cent-

ral bank money. If the interest rate on central bank money is set correctly,

shadow banks and traditional banks become indifferent between debt and

equity finance. This reduces the negative externality and improves financial

stability because shadow banks issue less uninsured deposits.

Finally, the results in Chapter 5 highlight that foreign borrowing should

be matched by an increase in export capacity because otherwise the borrow-

ing region will inevitably run into solvency problems. In our model solvency


214 Chapter 6

problems are prevented by introducing a debt-elastic interest rate, but in the

run up to the global financial crisis, Southern borrowing rates were largely

unaffected by their accumulating external debt levels. We examined vari-

ous structural reforms in the context of the euro area. Fiscal policy would

have offered a fairly straightforward tool to lean against excessive private

borrowing. Also a deepening, or liberalization, of the tradable sector might

shift production towards the more productive tradable sector.

6.3 Future research

In recent years, DSGE models have been implemented frequently to inform

policy makers about the potential impact of various policy measures. DSGE

models are especially advantageous to perform counterfactual experiments

when no data is available. New policy instruments, for example, cannot be-

nefit from past experiences and therefore rely extensively on the insights

generated by these models. In this thesis we highlighted various policy im-

plications using DSGE models with an independent role for the availability

and allocation of credit. However, the findings in this thesis also suggest

various directions for future research. Three possible directions stand out.

First, throughout this thesis, the capitalization of the banking sector is an

important variable that affects monetary transmission. An important feature

of bank equity that we ignored is that equity holder have limited liability.

The concept of limited liability might be important to understand how reg-

ulation affects bank incentives regarding e.g. risk taking and their leverage

choice, but also how these incentives change when banks are undercapital-

ized.

Second, since the global financial crisis, changes in the monetary stance

are predominantly determined by unconventional measures like forward

guidance or quantitative easing. In this thesis we focused on conventional

monetary policy and show that conventional monetary transmission is im-

peded when the banking sector is undercapitalized. Whether unconven-

tional measures also become ineffective or whether these measures can re-


Conclusion 215

store monetary transmission when banks are undercapitalized is, however,

unclear.

Finally, in this thesis we argued that, in particular, growth of mortgage

loans is an important determinant for the build-up of imbalances. Inelastic

housing supply and the inability to trade houses are responsible for large

fluctuations in house prices and mortgage supply. However, these features

of the housing market do not explain the dynamics that led to the build-up

of imbalances in the housing market and how these imbalances eventually

caused the bust. It is important to examine these dynamics further to be

able to inform policy makers about how to respond to the build-up of these

imbalances.


References

Adjemian, S., H. Bastani, M. Juillard, F. Mihoubi, G. Perendia, M. Ratto, and

S. Villemot (2011). Dynare: Reference manual, version 4. Dynare Working

Papers 1, CEPREMAP.

Adrian, T. and A. B. Ashcraft (2012). Shadow banking regulation. Annual

Review of Financial Economics 4(1), 99–140.

Adrian, T. and H. S. Shin (2009). Money, liquidity, and monetary policy.

American Economic Review 99(2), 600–605.

Agenor, P.-R. and R. Zilberman (2015). Loan loss provisioning rules, procyc-

licality, and financial volatility. Journal of Banking & Finance 61(December),

301–315.

Akerlof, G. A. (1970). The market for “lemon”: Quality uncertainty and the

market mechanism. Quarterly Journal of Economics 84(3), 488–500.

Albertazzi, U. and L. Gambacorta (2009). Bank profitability and the business

cycle. Journal of Financial Stability 5(4), 393–409.

Arellano, M. and O. Bover (1995). Another look at the instrumental variable

estimation of error-components models. Journal of Econometrics 68(1), 29–

51.

Arrow, K. J. and G. Debreu (1954). Existence of an equilibrium for a compet-

itive economy. Econometrica 22(3), 265–290.


218 REFERENCES

Baldwin, R. and F. Giavazzi (2015). The eurozone crisis: A consensus view

of the causes and a few possible solutions. http://voxeu.org/article/eurozone-

crisis-consensus-view-causes-and-few-possible-solutions Date last accessed: 7

August 2017.

Benes, J. and M. Kumhof (2015). Risky bank lending and countercyclical

capital buffers. Journal of Economic Dynamics and Control 58(September),

58–80.

Benigno, G. and L. Fornaro (2014). The financial resource curse. Scandinavian

Journal of Economics 116(1), 58–86.

Berger, A. N. and C. H. Bouwman (2013). How does capital affect bank

performance during financial crises? Journal of Financial Economics 109(1),

146–176.

Berger, A. N., A. Demirguc-Kunt, R. Levine, and J. G. Haubrich (2004). Bank

concentration and competition: An evolution in the making. Journal of

Money, Credit and Banking 36(3), 433–451.

Berger, H. and V. Nitsch (2014). Wearing corset, losing shape: The euro’s

effect on trade imbalances. Journal of Policy Modeling 36(1), 136–155.

Bernanke, B. (2005). The global saving glut and the U.S. current account

deficit. Sandridge Lecture, Virginia Association of Economics, Richmond,

Virginia, March 10.

Bernanke, B. S. and M. Gertler (1989). Agency costs, net worth, and business

fluctuations. American Economic Review 79(1), 14–31.

Bernanke, B. S. and M. Gertler (1995). Inside the black box: The credit chan-

nel of monetary policy transmission. Journal of Economic Perspectives 9(2),

27–48.

Bernanke, B. S., M. Gertler, and S. Gilchrist (1999). The financial accelerator

in a quantitative business cycle framework. In J. B. Taylor and M. Wood-

ford (Eds.), Handbook of Macroeconomics, Volume 1C, pp. 1341–1393. El-

sevier, Amsterdam.


REFERENCES 219

Bettendorf, T. and M. A. Leon-Ledesma (2015). German wage moderation

and european imbalances: Feeding the global VAR with theory. Bundes-

bank Discussion Paper 15/2015.

Bikker, J. A. and P. A. Metzemakers (2005). Bank provisioning behaviour

and procyclicality. Journal of International Financial Markets, Institutions and

Money 15(2), 141–157.

Blanchard, O. and F. Giavazzi (2002). Current account deficits in the euro

area: The end of the Feldstein-Horioka puzzle? Brookings Papers on Eco-

nomic Activity 2002(2), 147–186.

Boileau, M. and M. Normandin (2008). Closing international real business

cycle models with restricted financial markets. Journal of International

Money and Finance 27(5), 733–756.

Bolt, W., L. de Haan, M. Hoeberichts, M. R. van Oordt, and J. Swank (2012).

Bank profitability during recessions. Journal of Banking & Finance 36(9),

2552–2564.

Borio, C., E. Kharroubi, C. Upper, and F. Zampolli (2016). Labour real-

location and productivity dynamics: Financial causes, real consequences.

Bank for International Settlements Working Paper 534.

Borio, C. and P. Lowe (2001). To provision or not to provision. BIS Quarterly

Review 9(September), 36–48.

Bouvatier, V. and L. Lepetit (2008). Banks procyclical behavior: Does provi-

sioning matter? Journal of International Financial Markets, Institutions and

Money 18(5), 513–526.

Bouvatier, V. and L. Lepetit (2012). Provisioning rules and bank lending: A

theoretical model. Journal of Financial Stability 8(1), 25–31.

Brooks, S. P. and A. Gelman (1998). General methods for monitoring con-

vergence of iterative simulations. Journal of Computational and Graphical

Statistics 7(4), 434–455.


220 REFERENCES

Brunnermeier, M. K. (2009). Deciphering the liquidity and credit crunch

2007–2008. Journal of Economic Perspectives 23(1), 77–100.

Brunnermeier, M. K. and L. H. Pedersen (2009). Market liquidity and fund-

ing liquidity. Review of Financial Studies 22(6), 2201–2238.

Brunnermeier, M. K. and Y. Sannikov (2014). A macroeconomic model with

a financial sector. American Economic Review 104(2), 379–421.

Bushman, R. M. and C. D. Williams (2012). Accounting discretion, loan loss

provisioning, and discipline of banks risk-taking. Journal of Accounting

and Economics 54(1), 1–18.

Caballero, R. J. (2010). Macroeconomics after the crisis: Time to deal with the

pretense-of-knowledge syndrome. Journal of Economic Perspectives 24(4),

85–102.

Caballero, R. J., E. Farhi, and P.-O. Gourinchas (2008). An equilibrium

model of global imbalances and low interest rates. American Economic

Review 98(1), 358–393.

Calvo, G. A. (1983). Staggered prices in a utility-maximizing framework.

Journal of Monetary Economics 12(3), 383–398.

Canova, F. and M. Ciccarelli (2013). Panel vector autoregressive models:

A survey. In T. B. Fomby, L. Kilian, and A. Murphy (Eds.), VAR Models

in Macroeconomics–New Developments and Applications: Essays in Honor of

Christopher A. Sims, Volume 32, pp. 205–246. Emerald Group Publishing

Limited, Bingley.

Cavallo, M. and G. Majnoni (2002). Do banks provision for bad loans in

good times? Empirical evidence and policy implications. In R. M. Levich,

G. Majnoni, and C. M. Reinhart (Eds.), Ratings, Rating Agencies and the

Global Financial System, Volume 9, pp. 319–342. Springer, New York.

Cavelaars, P. (2006). The output and price effects of enhancing services-

sector competition in a large open economy. European Economic Re-

view 50(5), 1131–1149.


REFERENCES 221

Cecchetti, S. G. and E. Kharroubi (2015). Why does financial sector growth

crowd out real economic growth? Bank for International Settlements

Working Paper 490.

Cette, G., J. Fernald, and B. Mojon (2016). The pre-great recession slowdown

in productivity. European Economic Review 88(September), 3–20.

Chari, V. V., P. J. Kehoe, and E. R. McGrattan (2007). Business cycle account-

ing. Econometrica 75(3), 781–836.

Christiano, L. J., M. Eichenbaum, and C. L. Evans (1999). Monetary policy

shocks: What have we learned and to what end? In J. B. Taylor and

M. Woodford (Eds.), Handbook of Macroeconomics, Volume 1A, pp. 65–148.

Elsevier, Amsterdam.

Christiano, L. J., M. Eichenbaum, and C. L. Evans (2005). Nominal rigidities

and the dynamic effects of a shock to monetary policy. Journal of Political

Economy 113(1), 1–45.

Christiano, L. J., R. Motto, and M. Rostagno (2014). Risk shocks. American

Economic Review 104(1), 27–65.

Clarida, R., J. Gali, and M. Gertler (1999). The science of monetary policy:

A new Keynesian perspective. Journal of Economic Literature 37(4), 1661–

1707.

Clerc, L., A. Derviz, C. Mendicino, S. Moyen, K. Nikolov, L. Stracca,

J. Suarez, and A. Vardoulakis (2015). Capital regulation in a macroeco-

nomic model with three layers of default. International Journal of Central

Banking 11(3), 9–63.

Comunale, M. and J. Hessel (2014). Current account imbalances in the euro

area: Competitiveness or financial cycle? De Nederlandsche Bank Work-

ing Paper 443.

Curdia, V. and M. Woodford (2009). Conventional and unconventional mon-

etary policy. Centre for Economic Policy Research Discussion Paper 7514.


222 REFERENCES

Curdia, V. and M. Woodford (2010). Credit spreads and monetary policy.

Journal of Money, Credit and Banking 42(s1), 3–35.

DeAngelo, H. and R. M. Stulz (2015). Liquid-claim production, risk manage-

ment, and bank capital structure: Why high leverage is optimal for banks.

Journal of Financial Economics 116(2), 219–236.

Degryse, H. and S. Ongena (2008). Competition and regulation in the bank-

ing sector: A review of the empirical evidence on the sources of bank rents.

In A. V. Thakor and A. W. Boot (Eds.), Handbook of Financial Intermediation

and Banking, Volume 1, pp. 483–554. Elsevier, Amsterdam.

Del Negro, M., G. Eggertsson, A. Ferrero, and N. Kiyotaki (2010). The great

escape? A quantitative evaluation of the Fed’s non-standard policies. Fed-

eral Reserve Bank of New York Staff Reports 520.

Demirguc-Kunt, A., L. Laeven, and R. Levine (2004). Regulations, market

structure, institutions, and the cost of financial intermediation. Journal of

Money, Credit and Banking 36(3), 563–583.

Diamond, D. W. and P. H. Dybvig (1983). Bank runs, deposit insurance, and

liquidity. Journal of Political Economy 91(3), 401–419.

Dieppe, A., R. Legrand, and B. van Roye (2016). The BEAR toolbox.

European Central Bank Working Paper 1934.

Dixit, A. K. and J. E. Stiglitz (1977). Monopolistic competition and optimum

product diversity. American Economic Review 67(3), 297–308.

Eggertsson, G. B. and P. Krugman (2012). Debt, deleveraging, and the li-

quidity trap: A Fisher-Minsky-Koo approach. Quarterly Journal of Econom-

ics 127(3), 1469–1513.

Eichengreen, B. (2010). Imbalances in the euro area. Research Paper Univer-

sity of California, Berkeley, November.


REFERENCES 223

European Central Bank (2009). Recent developments in the retail bank in-

terest rate passthrough in the euro area. European Central Bank Monthly

Bulletin, August.

European Commission (2015). A deeper and fairer Single Market: Commis-

sion boosts opportunities for citizens and business. European Commis-

sion - Press release, 28 October 2015.

Fagan, G. and V. Gaspar (2007). Adjusting to the euro. European Central

Bank Working Paper 716.

Feldstein, M. (2012). The failure of the euro. Foreign Affairs 91(1), 105–116.

Fisher, I. (1933). The debt-deflation theory of great depressions. Economet-

rica 1(4), 337–357.

Fisher, I. (1961). The theory of interest. Kelley, Clifton.

Fonseca, A. R. and F. Gonzalez (2008). Cross-country determinants of bank

income smoothing by managing loan-loss provisions. Journal of Banking

& Finance 32(2), 217–228.

Freixas, X. and J.-C. Rochet (1997). Microeconomics of banking. Second edition.

MIT press, Cambridge, MA.

Gadatsch, N., N. Stahler, and B. Weigert (2016). German labor market and

fiscal reforms 1999 to 2008: Can they be blamed for intra-euro area imbal-

ances? Journal of Macroeconomics 50(December), 307–324.

Gaston, E. and M. I. Song (2014). Supervisory roles in loan loss provisioning

in countries implementing IFRS. International Monetary Fund Working

Paper 14/170.

Gennaioli, N., A. Shleifer, and R. W. Vishny (2013). A model of shadow

banking. Journal of Finance 68(4), 1331–1363.

Gerali, A., S. Neri, L. Sessa, and F. M. Signoretti (2010). Credit and banking in

a DSGE model of the euro area. Journal of Money, Credit and Banking 42(1),

107–141.


224 REFERENCES

Gertler, M. and P. Karadi (2011). A model of unconventional monetary

policy. Journal of Monetary Economics 58(1), 17–34.

Gertler, M. and N. Kiyotaki (2010). Financial intermediation and credit

policy in business cycle analysis. In M. W. Benjamin Friedman (Ed.),

Handbook of Monetary Economics, Volume 3, pp. 547–599. Elsevier, Ams-

terdam.

Gertler, M., N. Kiyotaki, and A. Prestipino (2016). Wholesale banking and

bank runs in macroeconomic modeling of financial crises. In H. U. John

B. Taylor (Ed.), Handbook of Macroeconomics, Volume 2, pp. 1345–1425. El-

sevier, Amsterdam.

Giavazzi, F. and L. Spaventa (2010). Why the current account may matter

in a monetary union: Lessons from the financial crisis in the euro area.

Centre for Economic Policy Research Discussion Papers 8008.

Gilbert, N. and S. Pool (2016). Sectoral allocation and macroeconomic im-

balances in EMU. De Nederlandsche Bank Working Paper 536.

Gilchrist, S. and B. Mojon (2017). Credit risk in the euro area. Forthcoming

in Economic Journal.

Gilchrist, S., R. Schoenle, J. Sim, and E. Zakrajsek (2017). Inflation dynamics

during the financial crisis. American Economic Review 107(3), 785–823.

Glaeser, E. L., J. Gyourko, and A. Saiz (2008). Housing supply and housing

bubbles. Journal of urban Economics 64(2), 198–217.

Goodfriend, M. and B. T. McCallum (2007). Banking and interest rates in

monetary policy analysis: A quantitative exploration. Journal of Monetary

Economics 54(5), 1480–1507.

Goodhart, C. (1988). The evolution of central banks, Volume 1. MIT press,

Cambridge, MA.


REFERENCES 225

Gopinath, G., S. Kalemli-Ozcan, L. Karabarbounis, and C. Villegas-Sanchez

(2017). Capital allocation and productivity in South Europe. Forthcoming

in Quarterly Journal of Economics.

Gorton, G. and G. Pennacchi (1990). Financial intermediaries and liquidity

creation. Journal of Finance 45(1), 49–71.

Green, R. K., S. Malpezzi, and S. K. Mayo (2005). Metropolitan-specific

estimates of the price elasticity of supply of housing, and their sources.

American Economic Review 95(2), 334–339.

Greenbaum, S. I., G. Kanatas, and I. Venezia (1989). Equilibrium loan pricing

under the bank-client relationship. Journal of Banking & Finance 13(2), 221–

235.

Greenwood, R., S. G. Hanson, and J. C. Stein (2015). A comparative-

advantage approach to government debt maturity. Journal of Finance 70(4),

1683–1722.

Greenwood, R., S. G. Hanson, and J. C. Stein (2016). The Federal Reserve’s

balance sheet as a financial-stability tool. In Designing Resilient Monetary

Policy Frameworks for the Future. Jackson Hole Symposium: Federal Re-

serve Bank of Kansas City.

Gurley, J. G. and E. S. Shaw (1960). Money in a Theory of Finance. Brookings

Institution Press, Washington.

Haan de, L. and J. W. van den End (2013). Banks’ responses to

funding liquidity shocks: Lending adjustment, liquidity hoarding and

fire sales. Journal of International Financial Markets, Institutions and

Money 26(October), 152–174.

Hahn, F. (1984). Equilibrium and macroeconomics. Blackwell, Oxford.

Hanson, S. G., A. Shleifer, J. C. Stein, and R. W. Vishny (2015). Banks as

patient fixed-income investors. Journal of Financial Economics 117(3), 449–

469.


226 REFERENCES

Holinski, N., C. J. Kool, and J. Muysken (2012). Persistent macroeconomic

imbalances in the euro area: Causes and consequences. Federal Reserve

Bank of St. Louis Review 94(1), 1–20.

Im, K. S., M. H. Pesaran, and Y. Shin (2003). Testing for unit roots in hetero-

geneous panels. Journal of Econometrics 115(1), 53–74.

Jacobs, J. P. A. M. and K. F. Wallis (2005). Comparing SVARs and SEMs: two

models of the UK economy. Journal of Applied Econometrics 20(2), 209–228.

Jimenez, G., S. Ongena, J.-L. Peydro, and J. Saurina Salas (2012). Macro-

prudential policy, countercyclical bank capital buffers and credit supply:

Evidence from the spanish dynamic provisioning experiments. European

Banking Center Discussion Paper 2012-011.

Jorda, O., M. Schularick, and A. M. Taylor (2015). Betting the house. Journal

of International Economics 96(Supplement 1), S2–S18.

Kalantzis, Y. (2015). Financial fragility in small open economies: firm balance

sheets and the sectoral structure. The Review of Economic Studies 82(3),

1194–1222.

Keynes, J. M. (1930). A treatise on money. Harcourt, Brace and company, New

York.

Keynes, J. M. (1936). General theory of employment, interest and money. Atlantic

Publishers & Distributors, New Delhi.

Kiyotaki, N. and J. Moore (1997). Credit chains. Journal of Political Eco-

nomy 105(21), 211–248.

Kollmann, R., M. Ratto, W. Roeger, and L. Vogel (2015). What drives the

German current account? And how does it affect other EU member states?

Economic Policy 30(81), 47–93.

Krishnamurthy, A. and A. Vissing-Jorgensen (2015). The impact of Treas-

ury supply on financial sector lending and stability. Journal of Financial

Economics 118(3), 571–600.


REFERENCES 227

Kydland, F. E. and E. C. Prescott (1982). Time to build and aggregate fluctu-

ations. Econometrica 50(6), 1345–1370.

Laeven, L. and G. Majnoni (2003). Loan loss provisioning and economic

slowdowns: too much, too late? Journal of Financial Intermediation 12(2),

178–197.

Levin, A., C.-F. Lin, and C.-S. J. Chu (2002). Unit root tests in panel data:

asymptotic and finite-sample properties. Journal of Econometrics 108(1),

1–24.

Love, I. and L. Zicchino (2006). Financial development and dynamic invest-

ment behavior: Evidence from panel VAR. Quarterly Review of Economics

and Finance 46(2), 190–210.

Lucas, R. E. (1976). Econometric policy evaluation: A critique. In Carnegie-

Rochester conference series on public policy, Volume 1, pp. 19–46. Elsevier,

Amsterdam.

Mankiw, N. G. (2006). The macroeconomist as scientist and engineer. Journal

of Economic Perspectives 20(4), 29–46.

Mano, R. C. and M. Castillo (2015). The level of productivity in traded and

non-traded sectors for a large panel of countries. International Monetary

Fund Working Paper 15/48.

Mian, A. and A. Sufi (2014). House of debt: How they (and you) caused the Great

Recession, and how we can prevent it from happening again. University of

Chicago Press, Chicago.

Mian, A. R., A. Sufi, and E. Verner (2016). Household debt and business

cycles worldwide. National Bureau of Economic Research Working Paper

21581.

Mierau, J. O. and M. Mink (2016). A descriptive model of banking and ag-

gregate demand. De Nederlandsche Bank Working Paper 500.


228 REFERENCES

Mink, M. (2016). Aggregate liquidity and banking sector fragility. De Neder-

landsche Bank Working Paper 534.

Minsky, H. P. (1986). Stabilizing an unstable economy. Yale University Press,

New Haven.

Modigliani, F. and M. H. Miller (1958). The cost of capital, corporation fin-

ance and the theory of investment. American Economic Review 48(3), 261–

297.

Moreira, A. and A. Savov (2014). The macroeconomics of shadow banking.

National Bureau of Economic Research Working Paper 20335.

Obstfeld, M. and K. Rogoff (1995). Exchange rate dynamics redux. Journal

of Political Economy 103(3), 624–660.

Ozhan, G. K. (2017). Financial intermediation, resource allocation, and mac-

roeconomic interdependence. University of St Andrews School of Eco-

nomics and Finance Discussion Paper 1704.

Paries, M. D., C. K. Sørensen, D. Rodriguez-Palenzuela, et al. (2011). Macroe-

conomic propagation under different regulatory regimes: Evidence from

an estimated DSGE model for the euro area. International Journal of Central

Banking 7(4), 49–113.

Patinkin, D. (1961). Financial intermediaries and the logical structure of

monetary theory: A review. The American Economic Review 51(1), 95–116.

Piton, S. (2015). Monetary integration and the nontradable sector. Paper

presented at the European Central Bank Forum on Central Banking 2015.

Pool, S. (2016). Credit defaults, bank lending and the real economy. De

Nederlandsche Bank Working Paper 518.

Pool, S., L. de Haan, and J. P. A. M. Jacobs (2015). Loan loss provisioning,

bank credit and the real economy. Journal of Macroeconomics 45, 124–136.


REFERENCES 229

Pozsar, Z., T. Adrian, A. B. Ashcraft, and H. Boesky (2010). Shadow banking.

Federal Reserve Bank of New York Staff Reports 458.

Reis, R. (2013). The Portuguese slump and crash and the euro crisis. Brook-

ings Papers on Economic Activity 172(Fall), 143–210.

Romer, P. (2016). The trouble with macroeconomics, delivered January 5,

2016 as the Commons Memorial Lecture of the Omicron Delta Epsilon

Society. Forthcoming in The American Economist.

Rothschild, M. and J. Stiglitz (1976). Equilibrium in competitive insurance

markets: An essay on the economics of imperfect information. Quarterly

Journal of Economics, 629–649.

Saiz, A. (2010). The geographic determinants of housing supply. Quarterly


Schmitt-Grohe, S. and M. Uribe (2003). Closing small open economy models.

Journal of International Economics 61(1), 163–185.

Sharpe, S. A. (1990). Asymmetric information, bank lending, and impli-

cit contracts: A stylized model of customer relationships. Journal of Fin-

ance 45(4), 1069–1087.

Shin, H. S. (2010). Risk and liquidity. Oxford University Press, Oxford.

Shin, H. S. (2014). Bank capital and monetary policy transmission. Panel

remarks at The ECB and its Watchers XVII conference, Frankfurt.

Smets, F. and R. Wouters (2003). An estimated dynamic stochastic general

equilibrium model of the euro area. Journal of the European Economic Asso-

ciation 1(5), 1123–1175.

Smets, F. and R. Wouters (2007). Shocks and frictions in US business cycles:

A Bayesian DSGE approach. American Economic Review 97(3), 586–606.

Sørensen, C. K. and T. Werner (2006). Bank interest rate pass-through in the

euro area: A cross country comparison. European Central Bank Working

Paper 580.


230 REFERENCES

Stein, J. C. (2012). Monetary policy as financial-stability regulation. Quarterly


Stiglitz, J. E. (2011). Rethinking macroeconomics: What failed, and how to

repair it. Journal of the European Economic Association 9(4), 591–645.

Stockman, A. C. and L. L. Tesar (1995). Tastes and technology in a two-

country model of the business cycle: Explaining international comove-

ments. American Economic Review 85(1), 168–185.

Svensson, L. E. (1997). Inflation forecast targeting: Implementing and mon-

itoring inflation targets. European Economic Review 41(6), 1111–1146.

Sy, M. (2016). Overborrowing and balance of payments imbalances in a

monetary union. Review of International Economics 24(1), 67–98.

Thornton, H. (1802). An Enquiry into the Nature and Effects of the Paper Credit

of Great Britain. Edited with an Introduction by F. A. v. Hayek., Rinehart

& Company, Inc., 1939, New York.

Timmer, M. P., E. Dietzenbacher, B. Los, R. Stehrer, and G. J. Vries (2015).

An illustrated user guide to the world input–output database: The case

of global automotive production. Review of International Economics 23(3),

575–605.

Townsend, R. M. (1979). Optimal contracts and competitive markets with

costly state verification. Journal of Economic theory 21(2), 265–293.

Wicksell, K. (1898). Interest and Prices. Gustav Fischer, Jena.

Wong, T., T. Fong, K.-f. Li, and H. Choi (2011). Loan-to-value ratio as a mac-

roprudential tool-Hong Kong’s experience and cross-country evidence.

Monetary Authority Working Paper 01/2011.

Woodford, M. (2000). Monetary policy in a world without money. Interna-

tional Finance 3(2), 229–260.


REFERENCES 231

Woodford, M. (2010). Financial intermediation and macroeconomic ana-

lysis. Journal of Economic Perspectives 24(4), 21–44.

Woodford, M. and C. E. Walsh (2005). Interest and prices: Foundations of a

theory of monetary policy. Cambridge University Press, Cambridge.

Zilberman, R. and W. Tayler (2014). Financial shocks, loan loss provisions

and macroprudential stability. Lancaster University Economics Working

Paper 23.


Summary

This thesis focusses on credit supply. We look at the consequences of changes

in the amount of credit supply for the macro-economy and at factors that af-

fect the amount of credit supply. The importance of credit supply for the real

economy was stressed during the 2008-2009 financial crisis. After the out-

break of the financial crisis, banks decreased credit supply and thereby put a

hold on economic growth. However, the causes of the financial crisis lie well

ahead of the outbreak. In particular, credit appeared to be structurally miss-

allocated which caused macroeconomic imbalances (e.g. the bubble in the

housing sector) that culminated in the financial crisis. After the start of the

financial crisis mainstream macroeconomic models offered few clues that

could explain why credit was structurally miss-allocated and why banks

ceased new lending. In this thesis we examine several novel mechanisms

that can explain these events.

In Chapter 2 we analyze the impact of credit default risk on bank lend-

ing. We show that during business cycle upturns bank loan loss provision-

ing is insufficient to cover future credit default losses. As a consequence, in

an economic downturn, when losses in the loan portfolio are high, banks

have accumulated insufficient buffers to cover their losses. In an economic

downturn banks start to build buffers nonetheless. This puts a break on

credit supply and amplifies the economic downturn. Provisioning for ex-

pected losses in the loan portfolio therefore causes pro-cyclical dynamics in

the real economy.

In Chapter 3 we extend the analysis of Chapter 2 to examine the im-


234 Summary

pact of credit defaults on the banks. We show that as a consequence of these

defaults the value of bank equity—the shareholders’ value—declines. The

central bank lowers the policy rate to attenuate the decline in economic

activity. Consequently, the borrowing rate (the funding costs) for banks de-

clines. However, banks would like, or are obliged by the bank supervisor,

to accumulate more bank equity and keep the lending rate (the revenues)

high. The increase in the spread between borrowing and lending rates al-

lows banks to increase their profit margin and accumulate more bank equity.

The decline of the policy rate, however, does not pass through to the real eco-

nomy. The effectiveness of monetary policy is therefore impeded and credit

supply declines strongly.

To ensure sufficient bank equity, also during an economic downturn, we

advise banks to build buffers in good times. If these capital buffers turn

out to be insufficient, a mandatory bank recapitalization can restore the ef-

fectiveness of monetary policy. A bank recapitalization can, however, cause

moral hazard. The bank takes, for example, more risk when the government

promises ex ante to bail-out the bank when it fails. For this reason, to minim-

ize the looming costs of moral hazard, we suggest to recapitalize the bank

by means of a mandatory equity issuance. This will ascribe the costs of a

recapitalization to the current shareholders who will therefore prevent the

bank from taking excessive risks.

In Chapters 4 and 5 we examine the role of credit allocation in the build-

up of imbalances. These imbalances could, once winded down, adversely

impact bank capitalization and deteriorate future credit supply. To prevent

the build-up of imbalances credit should be allocated efficiently and pro-

ductively. In these chapters we show, however, that when credit supply

suddenly increases, credit tends to flow typically to sectors that produce

goods that are both internationally hardly tradeable and have a low supply

elasticity (the percentage change in the quantity of a good supplied due to a

percentage change in the price of that good). This type of goods experiences

a relative strong price increase when credit supply suddenly increases. The

higher prices enable borrowers to pledge these goods as collateral for new


Summary 235

lending. These characteristics are illustrative for the real estate sector.

The build-up of imbalances in the real estate sector can be partially pre-

vented by tightening credit constraints for mortgage loans. Banks are in this

case simply not allowed to supply additional credit to finance a house. One

of our suggestions is to restrict the maximum admissible loan-to-value ratio

to create a precautionary buffer against house price fluctuations. A tighten-

ing of this type of constraint re-allocates bank lending towards more pro-

ductive business investment like machinery and equipment. This can have

a positive effect on economic growth in general.

Chapter 4 also shows how the growth of the market for mortgage loans

is related to the growth of the unregulated banking sector. The latter sec-

tor, also called the shadow banking sector, was mainly responsible for the

global financial crisis in 2008-2009. In itself, strong growth of the shadow

banking sector has no adverse consequences for financial or economic sta-

bility. However, the creation of shadow bank deposits which are not covered

by the deposit insurance scheme increases liquidity risk in the financial sys-

tem. Shadow banks do not pay for the costs when these risks materialize

because the shadow banking sector implicitly relies on liquidity support by

the central bank. As a consequence, shadow banks create too many unin-

sured deposits and more financial risk compared to socially optimal values.

In Chapter 5 we show that the build-up of macro-economic imbalances

in peripheral countries in the euro area go beyond the real estate and con-

struction sector. The bubble can best be classified as a boom in sectors that

produce internationally hardly tradeable products. The build-up of the bub-

ble was related to the decrease in real interest rates experienced by peri-

pheral countries in the euro area in the run-up to the European Monetary

Union. Interest rates declined for example, because peripheral countries in

the monetary union could gain from the credibility of the European Central

Bank causing interest rate and inflation risks to decline. We show that the

decline in real interest rates can also explain the divergence of current ac-

count positions—the difference between exports and imports of a country—

and wage rates between Northern and Southern Europe. Fiscal policy could


236 Summary

have offered a fairly straightforward tool to lean against excessive private

borrowing. However, we suggest that in particular a deepening, or liberal-

ization, of trade in the euro area can be beneficial to reduce macro-economic

imbalances.


Samenvatting (summary in

Dutch)

Dit proefschrift concentreert zich op kredietverlening. We kijken naar de

gevolgen van veranderingen in de hoeveelheid verleende kredieten op de

macro-economie en naar factoren die de hoeveelheid verleende kredieten

beınvloeden. Het belang van kredietverlening in de reele economie werd

benadrukt tijdens de financiele crisis van 2008-2009. Banken verminderden

na het uitbreken van de financiele crisis hun kredietverlening en hinder-

den daarmee de economische groei. De oorzaken van de financiele crisis

liggen echter ruim voor het uitbreken ervan. Met name krediet bleek struc-

tureel verkeerd te zijn toegewezen waardoor macro-economische oneven-

wichtigheden waren ontstaan (bijvoorbeeld de zeepbel op de woningmarkt)

die resulteerden in de financiele crisis. Macro-economische modellen bo-

den na het uitbreken van de financiele crisis weinig aanknopingspunten

om te verklaren waarom kredieten structureel verkeerd waren toegewezen

en waarom banken geen nieuwe kredieten meer wilden verstrekken. In dit

proefschrift onderzoeken we verschillende nieuwe mechanismen die deze

gebeurtenissen kunnen verklaren.

In Hoofdstuk 2 analyseren we het gevolg van kredietrisico’s op krediet-

verlening. We laten zien dat banken tijdens hoogconjunctuur te weinig voor-

zieningen treffen voor toekomstige verliezen op hun lening-portefeuille. Het

gevolg hiervan is dat banken in een economische neergang, wanneer ver-

liezen op de lening-portefeuille groot zijn, te weinig buffers hebben opge-


238 Samenvatting (Summary in Dutch)

bouwd om hun verliezen te dekken. Tijdens de economische neergang pro-

beren banken alsnog een buffer op te bouwen. Dit gaat ten koste van nieuwe

kredietverlening en versterkt daarmee de economische neergang. Het tref-

fen van voorzieningen voor verwachte verliezen op de lening-portefeuille

werkt daardoor procyclisch door in de reele economie.

In Hoofdstuk 3 breiden we de analyse van Hoofdstuk 2 verder uit door

grondiger te kijken naar de gevolgen voor de banken wanneer crediteuren

daadwerkelijk failliet gaan. We laten zien dat als gevolg van deze faillisse-

menten de waarde van het eigen vermogen—de aandeelhouderswaarde—

van een bank daalt. De centrale bank verlaagt de beleidsrente om een eco-

nomische neergang af te wenden. Hierdoor daalt de inleenrente (de finan-

cieringskosten) voor banken. Banken willen echter, of moeten van de toe-

zichthouder, meer eigen vermogen opbouwen en houden de uitleenrente

(de opbrengsten) hoog. Het toegenomen verschil tussen de inleen- en uit-

leenrente stelt banken in staat om meer winst te maken en dus meer eigen

vermogen op te bouwen. De daling van de beleidsrente werkt echter niet

door in de reele economie. De effectiviteit van het monetaire beleid is dus

verzwakt en de kredietverlening daalt sterk.

Om te garanderen dat banken voldoende eigen vermogen hebben, ook

tijdens een economische neergang, adviseren we banken om in goede tij-

den buffers op te bouwen. Mochten deze buffers onvoldoende blijken, dan

is een verplichte bankherkapitalisatie een effectieve manier om de effecti-

viteit van het monetaire beleid te herstellen. Bankherkapitalisaties kunnen

echter gepaard gaan met moreel risico. De bank neemt bijvoorbeeld meer

risico wanneer de overheid van te voren belooft de bank te redden wanneer

het mis gaat. Om moreel risico te voorkomen, stellen we voor om de bank te

herkapitaliseren door middel van een verplichte aandelenemissie. Hierdoor

komen de kosten van de herkapitalisatie bij de huidige aandeelhouders te

liggen. Deze zullen de bank daarom weerhouden van het nemen van exces-

sieve risico’s.

In Hoofdstuk 4 en 5 onderzoeken we de effecten van de allocatie van

kredietverlening in de opbouw van macro-economische onevenwichtighe-


Samenvatting (Summary in Dutch) 239

den. Deze onevenwichtigheden kunnen bij het barsten van een zeepbel een

negatief effect hebben op het eigen vermogen van banken en daarmee op

de toekomstige kredietverlening. Om deze onevenwichtigheden te voorko-

men zullen kredieten efficient en productief gealloceerd moeten worden.

In hoofdstuk 4 en 5 laten we zien dat wanneer de kredietverlening plotse-

ling toeneemt, kredieten in het bijzonder naar sectoren gaan die goederen

produceren die internationaal moeilijk verhandelbaar zijn en een lage aan-

bodelasticiteit (de procentuele verandering van de aangeboden hoeveelheid

van een goed als gevolg van een procentuele prijsverandering van dat goed)

hebben. Dit type goederen ondervindt namelijk na een toename van de kre-

dietverlening een relatief grote prijsstijging. De hogere prijzen maken het

vervolgens eenvoudiger om deze goederen als onderpand te gebruiken voor

nieuwe leningen. Deze karakteristieke eigenschappen zijn typerend voor de

huizensector.

De opbouw van onevenwichtigheden in de huizensector kan gedeelte-

lijk voorkomen worden door de hypotheekvoorwaarden aan te scherpen.

Banken mogen dan simpelweg minder krediet verstrekken voor de aankoop

van een huis. We pleiten, bijvoorbeeld, voor een vermindering van de maxi-

maal toegestane hypotheekschuld ten opzichte van de waarde van het huis.

Dit creeert een buffer die beschermt tegen toekomstige huisprijsfluctuaties.

Een aanscherping van dergelijke hypotheekvoorwaarden leidt bankkrediet

ook naar meer productieve bedrijfsinvesteringen zoals machines en appara-

tuur. Dit kan positieve gevolgen hebben voor de economische groei in ruime

zin.

In Hoofdstuk 4 laten we ook zien dat de groei van de hypotheekmarkt

gerelateerd is aan de groei van de niet-gereguleerde bankensector. Deze sec-

tor, ook wel de schaduwbanksector genoemd, was hoofdzakelijk verant-

woordelijk voor de financiele crisis in 2008-2009. Op zichzelf heeft sterke

groei van de schaduwbanksector geen negatieve gevolgen voor financiele

en/of economische stabiliteit. Echter, de creatie van deposito’s die niet ge-

dekt zijn door het depositogarantiestelsel verhoogt liquiditeitsrisico’s in het

financiele systeem. De schaduwbanken draaien niet op voor de economi-


240 Samenvatting (Summary in Dutch)

sche kosten wanneer deze risico’s materialiseren. De schaduwbanksector

vertrouwt namelijk impliciet op de liquiditeitsgaranties van de centrale bank.

Hierdoor creeren schaduwbanken meer ongedekte deposito’s en meer fi-

nanciele risico’s dan optimaal is voor een economie.

Tot slot laten we in Hoofdstuk 5 zien dat de opbouw van macro-econo-

mische onevenwichtigheden in perifere landen van het eurogebied meer

was dan alleen een zeepbel in de huizenmarkt. Een betere omschrijving is

een zeepbel in sectoren die internationaal moeilijk verhandelbare goederen

produceren. De zeepbel ontstond doordat reele rentes in perifere landen van

het eurogebied daalden in de aanloop naar de Europese Muntunie. Rentes

daalden onder andere omdat perifere landen in de muntunie konden profi-

teerden van de geloofwaardigheid van de Europese Central Bank waardoor

rente- en inflatierisico’s afnamen. We laten zien dat de daling in de reele

rente ook een verklaring biedt voor het oplopende tekort op de lopende

rekening—het verschil tussen de export en de import van een land—en de

stijgende lonen in deze landen. Fiscale consolidatie had het private spaar-

tekort kunnen compenseren. Echter, we suggereren dat vooral een verdere

liberalisatie van de handel in het eurogebied de macro-economische one-

venwichtigheden doet afnemen.

University of Groningen Credit supply and macroeconomic … · 2018. 3. 12. · 517798-L...

Documents

Transcript of University of Groningen Credit supply and macroeconomic … · 2018. 3. 12. · 517798-L...